Heat 1 tablespoon of sesame oil in a skillet over medium-high heat.
Add in the chopped onion, and cook for 2-3 minutes until it begins to soften.
Pour the riced broccoli into the skillet, and stir to combine the onion and broccoli. Cook and stir the riced broccoli for 4-6 minutes, or until it reaches the desired level of doneness.
Once the riced broccoli is just about done cooking, add in 3-4 tablespoons of soy sauce, and stir to combine.
With the broccoli off to one side of the skillet, and crack two large eggs into the pan.
Stir them around to scramble them, and mix them into the broccoli fried rice as they finish cooking.
Garnish with freshly chopped green onions and sesame seeds if desired.