Preheat oven to 400° F; position rack in middle of oven.
In a large bowl, whisk together eggs; set aside.
In a 10-inch ovenproof nonstick skillet, heat oil over medium heat until shimmering. Add onion and cook, stirring, until it begins to soften, 4 minutes. Add broccoli and cook, stirring, until warmed through, 2 minutes more. Season to taste with salt and pepper.
Pour eggs over vegetables, covering them evenly; cook, gently lifting and pushing cooked edges toward center, allowing liquid egg to fill space, about 4 minutes. Sprinkle with cheese and transfer pan to oven. Bake until frittata is golden brown and puffed up, 12-15 minutes (frittata should be just slightly soft in center). Transfer frittata to a cutting board, cut in 6 wedges and serve immediately.