Creamy Chicken Sausage And Broccoli Pasta

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Ingredients

1 tablespoon olive oil
1 pound uncooked sweet italian chicken or turkey sausage, casings removed
1 medium yellow onion, medium dice
kosher salt
freshly ground black pepper
1 pound broccoli, stemmed and cut into 1-inch florets
1 pound dried fusilli or other short pasta
3/4 cup heavy cream
1/2 cup tightly packed finely grated parmesan cheese (about 1 1/2 ounces), plus more for serving