Cook the rice according to the package instructions. Keep warm.
Fill a large saucepan with water and bring it to a rolling boil. One by one, blanch the carrots, zucchini, cucumber, and radish for 1 minute and the bean sprouts for 2 1/2 minutes. Use a slotted spoon or sieve to remove them from the water, and drain fully. Season each vegetable with 1/2 teaspoon roasted sesame seed oil and soy sauce each, keeping the vegetables separate at all times.
Heat 1 tablespoon vegetable oil in a skillet over medium-high heat. Add the mushrooms and stir-fry until softened, 4 to 5 minutes. Dump the mushrooms in a bowl and season with 1/2 teaspoon each roasted sesame seed oil and soy sauce.
Return the skillet to medium-high heat. Add the spinach and sprinkle with 2 teaspoons water. Cook for a few minutes, stirring constantly, until the spinach has wilted. Remove the spinach, squeeze out any excess water, and season with 1/2 teaspoon each roasted sesame seed oil and soy sauce. (In Korea, these vegetables are served at room temperature, so don’t worry about keeping them warm.)
Return the skillet to medium-high heat, add the marinated beef and the marinade, and stir-fry until the sauce has reduced and the meat is cooked through, about 3 minutes, give or take depending on how thinly you sliced the beef. Move to a plate.
Wipe out the skillet or use a clean pan and fry the eggs to your liking.
Divvy the hot rice among 4 individual bowls. Place 1 egg in the center of the rice, then arrange the vegetables and meat around it. Sprinkle over some sesame seeds and salad greens or watercress, and serve with the gochujang sauce. (Advise guests to start with a couple of spoonfuls of the sauce and mix everything together well. Add more gochujang sauce to taste.)