Preheat your oven to 350°F.
Whisk together eggs, cream, salt, and pepper in a bowl. Stir in half the cheese.
Melt butter in an oven-safe skillet over medium heat. Add shallot, garlic, and broccoli. Cook until broccoli is tender, about 3-4 minutes.
Pour the egg mixture into the pan and cook for 1-2 minutes until edges start to set.
Top with remaining cheese and transfer to oven.
Bake for 12-15 minutes until just slightly jiggly in the center and golden brown on edges.