Add broccoli to a food processor. Pulse until broccoli resembles rice. Do not over process!
Heat a large wok or non-stick pan to a high heat. Add 2 teaspoons sesame oil. Once the oil is hot, add onion, garlic, and carrot. Season with salt and pepper. Use a wooden spoon to stir-fry veggies until fragrant, about 30 seconds. Add another two teaspoons of sesame oil and add broccoli. Again, season with a little bit of salt and pepper. Continue to stir-fry 3-4 minutes until broccoli begins to cook. Add remaining oil followed by rice. Continue to use the wooden spoon to stir-fry the mixture for another 2 minutes or until the veggies are all cooked.
Drizzle in soy sauce and sprinkle with garlic powder. Continue to cook another 2-3 minutes until sauce has coated all the rice and veggies. Reduce the heat to medium and make a well in the center of the mixture. Crack an egg in the middle and use the spoon to scramble the egg. Mix in to the rice.
Add green onions. Toss. Season to taste with salt and pepper. Serve hot.