Add 3 tablespoons of sesame oil to the pan and set over medium heat. Add the green onion, garlic, and ginger and cook, stirring often, until softened but not browned, 3 to 4 minutes. Add the riced cauliflower, 4 tablespoons of the soy sauce, 2 tablespoons hoisin sauce, 1 tablespoon oyster sauce, red pepper flakes, brown sugar, and 1/4 teaspoon salt. Cook, stirring often, for about 3 minutes. Add the peas and carrots and continue cooking until the cauliflower “rice” is tender-crisp and the vegetables are warmed through, a few minutes. Stir in the rice vinegar, sesame oil, green onions, nuts (if using) and eggs. Taste and adjust seasoning (adding the remaining tablespoon of soy sauce if necessary). Serve hot.