Soften the vegetables: Heat the oil in a large skillet over medium-low heat. Add the onion, green bell pepper, red bell pepper, mushroom and grated carrot. Cover the skillet and cook, stirring occasionally, until the vegetables are soft and the onion turns translucent.
Make the sauce: While the vegetables cook, combine the soy sauce, water, vegetable stock, sugar, Shaoxing wine, vegetarian oyster sauce, and dark soy sauce in a small saucepan over medium heat. Whisk gently until the sugar fully dissolves and the mixture comes to a light simmer.
Thicken the sauce: In a small bowl, mix the cornstarch with a little water until smooth. Slowly stir it into the simmering sauce and cook for about 1 minute, until the sauce thickens and becomes glossy. Remove from heat and set aside.
Prepare the egg mixture: In a large bowl, add the beaten eggs, mung bean sprouts, green onions, soy sauce, toasted sesame oil, and garlic powder. Stir until everything is evenly combined and well seasoned.
Combine eggs and vegetables: Add the cooked vegetables to the egg mixture and gently stir until the vegetables are evenly distributed throughout the eggs. Set the mixture aside briefly while you heat the pan.
Fry the egg foo young: Heat a small skillet over medium heat and add enough oil to lightly coat the bottom. Pour a portion of the egg mixture into the center of the pan and let it cook until the bottom turns golden brown. Carefully flip and cook the other side until fully set and lightly browned.
Drain and repeat: Transfer the cooked egg foo young to a paper towel-lined tray to absorb any excess oil. Repeat the process with the remaining egg mixture, adding more oil to the pan as needed between batches.
Serve and enjoy: Serve the vegetable egg foo young right away with warm rice, drizzle generously with the prepared sauce. Garnish with green onions and enjoy!