"I love the spicy, savory taste of Korean bibimbap, but I couldn't find a recipe here. I looked online and talked to some Korean friends, and this was the result. I hope you enjoy this dish as much as I have! To eat, just mix everything in the bowl together and enjoy with Korean hot chile sauce!"
Mix soy sauce, sugar, sesame oil, garlic, and ginger together in a bowl. Add beef brisket and cover with plastic wrap. Marinate in the refrigerator for for 30 minutes.
Rinse rice until water turns clear. Pour into a rice cooker and add 1 1/2 cups water. Seal and select setting according to manufacturer's instructions; cook until tender, 20 to 30 minutes. Keep warm.
Place mushrooms in a bowl of warm water. Soak for 20 minutes.
Coat eggplant with salt on all sides and allow to 'sweat,' about 10 minutes. Rinse with cool water.
Squeeze the water out of the re-hydrated shiitake mushrooms and slice into 1/4-inch strips.
Heat 2 tablespoons sesame oil in a skillet over medium-high heat. Saute mushrooms until lightly browned, about 4 minutes. Transfer to a covered plate to keep warm.
Saute eggplant in the same skillet until slightly softened, about 5 minutes. Transfer to the plate with the mushrooms.
Place squash in the hot skillet; cook and stir until slightly tender, about 5 minutes. Add to the plate with the eggplant and mushrooms; keep vegetables warm.
Saute carrots and broccoli in the skillet until slightly tender, about 6 minutes. Transfer to the plate with rest of the vegetables.
Bring a large pot of water to a boil. Add sprouts and cook uncovered until tender but still crispy, about 2 minutes. Drain in a colander and immediately immerse in ice water for several minutes to stop the cooking process. Drain.
Heat the same skillet over medium-high heat. Add marinated beef slices and saute until nicely browned and lightly pink in the center, about 7 minutes.
Place approximately 1 cup cooked rice in each bowl. Season with remaining sesame oil and vinegar. Pat rice down with a spoon to make a mound. Cover with a bed of lettuce. Add small mounds of cooked mushrooms, eggplant, squash, carrots, and broccoli on the lettuce around the edge of the bowl. Place beef in the center.
Heat the skillet over medium heat. Break eggs into skillet and season with salt. Cook until whites are just set and yolks are slightly runny, about 3 minutes. Place a sunnyside-up egg on top of the beef in each bowl. Top with radish and green onion.