Salami and Provolone Crustless Quiche

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2 tablespoons unsalted butter, at room temperature

2 tablespoons finely grated Parmesan

2 cups half-and-half

2 large eggs

2 large egg yolks

Kosher salt and freshly ground black pepper

Pinch of paprika

1 cup grated provolone

3/4 cup diced sliced salami

2 tablespoons chopped fresh basil, plus more for serving