In a very large saute pan or Dutch oven, heat the oil over medium heat. Add the Italian sausage and cook until browned and cooked through. Add the garlic and heat for about a minute, or until fragrant.

Pour in a small amount of the chicken broth, and use a spatula to deglaze the bottom of the pan. Pour in the remaining chicken broth and bring to a boil.

Stir in the orecchiette, breaking apart any pasta that's nesting together. Cover the pot and cook for 3 minutes. Stir in the broccoli. Cover and continue to cook for 8-10 minutes, stirring occasionally, until the pasta is soft and most of the liquid is absorbed.

Stir in the Parmesan, allowing it to melt. Season to taste with Kosher salt and fresh ground black pepper. Serve with more Parmesan on top.