Broccoli and Goat Cheese Crustless Quiche

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2 tablespoons unsalted butter, at room temperature, plus more, for the pie plate

2 tablespoons finely grated Parmesan

2 cups half-and-half

2 large eggs

2 large egg yolks

Pinch cayenne

Kosher salt and freshly ground black pepper

2 1/2 cups small broccoli florets

2/3 cup crumbled fresh goat cheese

2 tablespoons chopped fresh parsley