The first thing husband-and-wife team Kyle and Katina Connaughton did when they won their third Michelin star late last year was to throw on their hoodies and go to a Rancid gig as soon as the ceremony was over. To look at them, you wouldn't know they're a couple of die-hard punks. The Californian couple, based in Healdsburg in Sonoma County, own and run SingleThread – a closed-loop restaurant serving their flavour of Japanese-Californian cuisine.

Katina runs the organic farm where most of their produce is grown (she has a sticker on her laptop that says, "I brake for wildflowers"), while Kyle is in charge of the kitchen. The pair have been partners since they were teenage skate-rats in Los Angeles and have enjoyed a career that's taken them across the globe, from rural Japan to the Fat Duck laboratory in Brae, but California will always be home.

We met at a punk show when we were 15 and 16. [Katina] We've been living together for 26 years. I became a mother very young (I turned 19 a week after we had our first daughter, and I was 24 by the time we had our second) so I think I have this innate sense to nurture. Coming from LA to Japan, I really started to look around me. We were in a very rural area. My eyes just opened up to a new world. Then I started gardening and studying and everything started to make sense. To be able to nurture something from seed through maturity for me to it just felt so natural and comforting.

Moving from LA to Japan was definitely a leap. [Katina] Kyle had gone six weeks prior, so I moved with the girls. We had six suitcases, I had a girl in each hand trying to figure out how to push the luggage cart. I just remember being exhausted and confused. We got out there and we just carved out this life. It was extraordinary. It was the first time our youngest daughter had ever gone to school – she was the first foreigner to ever grace the halls. Both girls were. We were so remote and people were so warm and welcoming. It's unlike anywhere I've ever been. It was an incredible experience.

We don't consider SingleThread a Japanese restaurant. [Kyle] It's a Californian restaurant but we grow a lot of Japanese vegetables. It's not a rush of cream and butter sauces and bread. It's more seafood and vegetable-driven, a lot of Japanese flavours, a lot of Japanese seasonings. Our main methods of cooking are open fireplace and Japanese clay pots. We don't say we're a Japanese restaurant or it is Japanese cuisine but it's very familiar for someone who's Japanese.

We're very grounded in our farming and it really dictates so much of what we do. [Kyle] The interesting thing about farming is that you cannot force nature. Things take their time to grow. You have to pay attention to them, you have to nurture them, you have to amend the soil, you have to be thinking ahead. It's a very humbling experience. It builds a box from within: how you work, how you live ... and it's very important to have those parameters to work within because it just informs you as to what you can and can't do. That's very important for us.

We learned very early on in life together being ambitious, having big dreams and raising two children very young that we would always rely heavily on quality over quantity. [Katina] I think that we just really value our time together. And actually, this venture has allowed us to spend more time together than we ever had. I feel that that's really enriched our lives and has strengthened our relationship so much. [Kyle] It's this very symbiotic relationship. The restaurant relies on the farm side and the farm relies on the restaurant. The two only work when the other works well. The two are so intertwined that it creates a real sort of reliance, which is like the same in our relationship. Being a young cook and a young mother and having a young family ... you're just so broken, working hard and just trying to make it happen. [Katina] We don't get many days off, but when we do he's just the person I want to hang out with the most in this world.

2006-2011 was an exciting time at the Fat Duck [Kyle] It was really on top of the world at that time. I came to open and run the lab, which was all the menu development and the books and the presentations and all the crazy side-stuff. I came at a good time and I left at a good time. The years I was there were very exciting. It was the beginning of the TV stuff where it was really exciting and a lot of really good science was being done. And it was just fun. I think [Katina and I] learned a lot from being part of that trajectory and then watching where it leads. There's good and bad in all of it. My biggest takeaway from Heston [Blumenthal] was this real focus on the multi-sensory aspects of dining. At the Fat Duck everything that we did there was very much like, 'Here listen to this iPod' or 'Watch this' or 'We're going to tell you this story', or 'We're going to lay out the whole Alice in Wonderland thing for you'. It was this incredible narrative that was done in such a spectacular way. It was about lighting. It was about smell. It was about feel, it was about all of these things. But the big takeaway was about context. About having a really good story that you could connect people with.

After the Michelin awards we went to a punk show to see a band that we've been listening to since the '90s called Rancid. [Katina] We went to the gala and then we did a quick change, and threw our sweatshirts on. It could not have been more perfect. We're still punk rockers.

Myffy Rigby was a guest of Sonoma County Tourism.