Cut the chicken into thin 2-inch strips. Mix the marinating sauce and marinate the chicken for 20 minutes. Sauté in a skillet for 2 - 3 minutes over high heat.
Bring 1 cup of water to a boil with a tsp of salt. Blanch the bean sprouts and boil for 3 minutes. Drain quickly and shock in cold water to stop cooking. Drain again. Add 1 spoonful of the sauce and toss to coat the beansprout.
In a pot of salted boiling water, blanch the spinach until wilted, 30 - 40 seconds. Drain quickly and shock in cold water. Squeeze out water. Cut into 3-inch lengths. Toss with one spoon of the sauce.
Cut the zucchini in half lengthwise and then thinly slice crosswise. Generously sprinkle salt over sliced zucchinis and set aside for 10 - 15 minutes. Squeeze out excess liquid from salted zucchini by hand. Add sauce 1 spoonful of the sauce and sauté in a lightly oiled skillet for 1 - 2 minutes over medium high heat.
Cut the carrots into matchsticks. Sauté in a lightly oiled skillet for 1 - 2 minutes over medium high heat, sprinkling salt and pepper to taste.
Cut the shitake mushrooms into thin slices. Sauté and season with salt and pepper.
Combine all of the bibimbap sauce ingredients in a small bowl and mix thoroughly.
To assemble: Place a serving of rice in a big bowl. Nicely arrange a small amount of each prepared vegetable and chicken over the rice. Drizzle a little sesame oil over. Top with an egg fried sunny side up, roasted sesame seeds, and serve with the Bibimbap sauce.
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