Make cauliflower rice: put cauliflower in a food processor fitted with a shredder blade and process until completely shredded.
Heat the oil in a large non-stick frying pan over medium-high heat. Add chopped onion, bell pepper and carrot and cook, stirring occasionally, for 5 minutes.
Add cauliflower rice, soy sauce and pepper and mix until combined.
With a spatula, make a well in the middle of the frying pan and add 2 eggs to that space. Mix the eggs with the cauliflower rice mixture and cook, stirring constantly, for 3 minutes, or until the eggs and cauliflower are cooked through.