If using cauliflower heads: Grate the cauliflower in a food processor fitted with the grating disc. Alternatively, grate on the large holes of a box or hand-held grater. Set aside. (Skip this step if using "ready to cook" cauliflower rice.)
Heat EVOO/avocado oil for eggs in a large nonstick skillet over medium heat. Add the eggs and a pinch of salt and scramble until the eggs are cooked. Transfer to a small plate and set aside. Wipe the pan clean.
Add EVOO/avocado oil for cauliflower to the pan and set over medium heat. Add the light scallions, garlic, and ginger and cook, stirring often, until softened but not browned, 3 to 4 minutes. Add the grated cauliflower, soy sauce, red pepper flakes, and salt to taste (if needed). Cook, stirring often, for about 3 minutes.
Add the peas and carrots (optional) 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, dark green scallions and eggs. Serve hot.