Place oven rack in the center and preheat oven to 400°F.
Whisk eggs together in a medium bowl and set aside.
Heat oil in a large skillet over medium heat. Chop onion and broccoli; set aside separately.
Add onion to hot oil. Cook for 3-4 minutes to begin to soften. Add broccoli and cook for another 2 minutes. Sprinkle with salt and pepper.
Pour in eggs and cook for 3-4 minutes, pushing toward the center to begin to cook and allowing uncooked eggs to move around. If using an oven-proof skillet, sprinkle with cheese and toss skillet into oven. If not, transfer mixture to a greased baking dish, sprinkle with cheese, and then place in oven.
Bake for 12-15 minutes until eggs are puffed up and slightly browned.
Cut into squares and serve with tangerines on the side.