Heat 1 tablespoon of sesame oil in a large cast-iron skillet over medium-high heat. Add carrots and cook for about 5 minutes. Add garlic and peas and cook for 1 minute. Add cauliflower and soy sauce continuing to "stir fry" for 5 more minutes.
Using a wooden spoon, push cauliflower mixture to edges of the pan making a well in the middle. Turn down heat to medium-low. Add remaining sesame oil and eggs. Scramble the eggs cooking until done. Stir eggs into cauliflower fried rice.
Taste and add more soy sauce if desired. Top with green onion slices and serve.