Preheat your oven to 350°F.
In a medium bowl, whisk together the eggs, heavy cream, salt, and pepper until well blended. Stir in the cheese and set aside.
In a large, oven-proof skillet or Dutch oven, melt the butter over medium heat. Add the shallot, garlic, and broccoli and cook until just tender, about 3-4 minutes.
Spread the vegetables out around the pan, then gently pour the egg mixture into the pan.
Continued cooking for 1-2 minutes, or until the bottom just starts to firm up.
Place the pan in the oven and cook for about 12-15 minutes (add extra cheese on top at around 10-12 minutes, if desired, so that it has a few minutes to melt before the frittata is done cooking).
The frittata is done when it is just barely jiggly in the middle and golden brown along the edges and bottom.
Slice into 8 pieces and top with the green onions or parsley, if desired.