Prepare the sauce by combining all ingredients in a small bowl.
- Heat a small pan over medium heat. Add oil and cook each of the vegetable toppings in turn, until they just start to become tender, about 6 minutes for the carrots, 5 minutes for the mushrooms and 3 minutes for the bean sprouts. Use salt and pepper to taste.
- Fry the eggs on one side until the whites are firm but the yolks are still runny.
- Assemble the bowls by distributing the toppings among the serving bowls with rice. Drizzle with Bibimbap Sauce and sprinkle with sesame seeds.