In a large skillet over medium-low heat, add the oil. Once hot, add the onion, green bell peppers, red bell peppers, and grated carrot. Add the top to the skillet and cook until the vegetables are softened and the onion is translucent, occasionally stirring for 15 minutes.
While the vegetables are cooking, make the sauce. Place the soy sauce, water, chicken stock, sugar, wine, oyster sauce, and dark soy sauce into a small saucepan over medium heat.
Whisk until the sugar dissolves and bring to a simmer.
In a small bowl, whisk together the cornstarch and water.
Once at a simmer, slowly stream in the cornstarch slurry, whisking constantly. Continue to whisk until thickened, then take off heat.
To make the egg mixture, add the beaten eggs, bean sprouts, half of the green onions, soy sauce, sesame oil, and garlic powder to a large bowl and stir to combine.
Add the cooked vegetables and stir well, set aside.
Heat a small roughly 8-inch skillet over medium heat. Add enough oil to coat the bottom of the pan and pour ⅓ cup of the egg mixture into the center of the pan. Fry for 2-3 minutes until golden brown on the bottom. Carefully flip it over and continue to cook for another 2 minutes until browned on the bottom and cooked through.
Place the egg foo young on a sheet tray lined with paper towels to absorb any excess oil. Repeat with the remaining egg mixture, you may need to add more oil during the cooking process.
Serve immediately with your favorite sides and some of the sauce drizzled on top. Garnish with the remaining sliced green onions.