Make the marinade for the beef. Combine the soya sauce, sugars, garlic, spring onions and sesame seeds in a large bowl; add the sliced beef strips to the marinade, and season with salt and pepper. Cover and marinate in the fridge for at least 2 hours.
Bring the rice and water to the boil in a saucepan over high heat. Reduce heat to medium-low and cover; simmer until the rice is tender and the liquid has been absorbed, 20 to 25 minutes.
Preheat the oven to 220 C / Gas 7, and place 6 Korean stone bowls in the oven.
Combine shiitake mushrooms and 125ml hot water in a small bowl, and soak for about 10 minutes, until pliable. Trim off and discard the stems. Thinly slice the caps and set aside.
Bring a saucepan of water to the boil. Add spinach to the water just long enough to wilt the leaves, and then drain and pat dry; set aside. Combine cucumber and carrots in a bowl, and season with salt and pepper; set aside.
Warm a little sesame oil in a wok over a medium high heat then add the carrots and cucumber and cook and stir until softened. Remove from pan, and set aside. Add a small amount of sesame oil to the pan, and cook spinach in sesame oil for a minute or two. Remove spinach from pan,and set aside. Boil the beef marinade for 5 minutes until the liquid reduces in volume, then add the beef and cook for a few minutes, until no longer pink in the centre, about 4 to 5 minutes.
Transfer the stone bowls from the oven to suitable heat resistant surface. Brush each bowl with sesame oil to coat. Divide the rice into the bowls, and gently pack to the bottom (the rice should sizzle as you arrange). Arrange the cucumbers and carrots, bean sprouts, greens, shiitake mushrooms, and beef mixture over each potion of rice. Immediately before serving add one raw egg yolk to each bowl, drizzle with about a tablespoon of sesame oil, and top with the nori. Serve gochujang sauce as a condiment.
You can substitute courgette for the cucumber. For dolsot bibimbap, you can either fry the egg and place on top, or just add the raw egg yolk on top immediately before serving to allow the person eating to mix it in.