Mother made our kitchen cupboard in Copenhagen from reclaimed window frames. She's ascetic, minimalistic and was a Maoist, it's fair to say. She was very much into the Chinese revolution and everything Chinese, and fried a lot of rice. My brother and I used chopsticks from a very early age. I was interested only in desserts, but she never made any, although sometimes she put chocolate on rye bread in the school lunchbox. I'd try ways to eat the bread first and chocolate last. And there was sometimes the 15-minute ritual of stirring egg yolk with sugar to make an eggnog.

My brother and I had to do the dishes every night, so had endless fights because we both wanted to dry. I'd usually wash because he'd disappear to the toilet at the decisive moment. He'd also whip me with the tea towel. So there was a lot of shouting and screaming and smashing of glasses and plates, but my mother always made us continue. Whereas today, if my own kids were destroying my porcelain every evening, I'd probably let them off the hook and take over.

When I was nine I was stealing, with a friend, very sweet chewing gum from a supermarket, so our parents wondered why we constantly chewed and then it became very traumatic. We were made to go back to the supermarket with my friend's mum, to confess, very humiliatingly. We waited in line with the shoppers before explaining and apologising, although the cashier didn't give a fuck. (But it stopped us, we didn't do it again.)

When I was 12 my mother moved us into a commune. Eight families ate together every night, saving a lot of time on shopping and cooking. Each adult had to cook only twice a month and each child once a month. So – the very first time I cooked in my life – I had to make burgers for 30 or more people. And I wonder where my great fear of failure at cooking comes from.

My acting debut, at 17, was in the film Oviri, with Donald Sutherland as Paul Gauguin. Donald got vegetarian food delivered to the set every day from a top restaurant and this was a level of luxury I'd never imagined. I've since been amazed, on film sets, how there's always someone complaining about the catering. If I was at home I'd put some cheese on ryebread for lunch, a little smørrebrød, or dip a hard-boiled egg in salt. So, come on, what's to complain about?

Sarah Lund having an egg in The Killing was her pushing the boat out, really. And the chewing of nicotine gum was something the writer stole from me. I chewed nicotine for many, many years but actually stopped a few months ago. I miss it so much – the stimulation and just having something in my mouth a lot – that I might fall back any day.

It takes work as an actor to make eating something your character does. It's such a private or intimate act. In order to eat you have to be quite relaxed and I'm just not relaxed when performing. Swallowing on stage is extremely difficult. Once, during a break in a play rehearsal, a director saw me eating my liver pâté rye bread, wrapped in lunchbox paper, and said, "Can we use that in the scene?", so every night I had to eat my own lunch on stage.

I enjoy, every day, shopping for high-quality ingredients to cook with, far more than cooking with them. When I meet people who say they relax when cooking, I'm just so envious. When I serve my food to people, after all the panic, I apologise – as a reflex – and explain everything wrong with it. But I know my children will reject what I make anyway, except for four or five dishes which I therefore don't vary from. A lot of my friends are very good cooks. In fact everyone is a good cook compared to me.

I used to hide desserts from my brother and now I can hide them from my children. I can play righteous Sugar Saint with them and then – as soon as they're not looking – go hypocritically mad with the cookies. We know so much about food nowadays – what's "good" and what's "bad" – that it's become almost religious. I think the closest modern western people get to the feeling of being sinners is not about moral actions or thoughts, but things like "I've used a lot of butter in this".

When I got my diagnosis of breast cancer [in late 2012] I became obsessed with the thought that I must have eaten something that caused this, and started reading a lot about what I shouldn't and should eat, although now I'm relaxing a bit more. I had terrible, terrible nausea from the first three chemo treatments and afterwards couldn't taste anything – even water – and then everything tasted wrong. The illness made me a lot more aware of how enjoyment of this precious life boils down to simple things like being able to taste and enjoy food.

Making [the upcoming TV drama] Fortitude we stayed in the very far east of Iceland in a small, small town called Reyðarfjörður and thought, "What are we going to do here?" But it had the most amazingly wonderful restaurant called the Farm, which had its own cows, sheep and chickens – and homemade ice-cream – and was located by the fjord with breathtaking views. I couldn't close my trousers when I had to go home. The only actor who cooked was Stanley Tucci, whose trailer kitchen was full of food. I really enjoyed his frittata.

I find it funny that, in Denmark, what Brits call a Danish pastry is known as Wienerbrød – meaning bread from Vienna. I don't know why no one will claim ownership, because they're lovely. In Denmark we call the one with yellow curd in the middle bager dårlige øje – meaning baker's bad eye, which isn't kind to bakers either, I think. But we have the eating word Velbekomme (meaning "I hope the food serves you well") which you lack an equivalent to. There is an extremely popular, indulgent cookery show in Denmark presented by the Price brothers, one of whom wrote Borgen. But my favourite broadcast in Denmark was your Two Fat Ladies.

Holburg 19 is my local cafe – a very lovely, very relaxed place. I live beside the Royal Danish Theatre [in Copenhagen], and have views across the harbour to [the restaurant] Noma. People travel from Britain to eat there, while I'm standing watching it every day but have still never been there. I really should because it's elevated our traditional peasant food of cabbage and porridge to an art form.

Sofie Gråbøl is in the James Plays at the National Theatre, London from September