Orecchiette with Sausage and Broccoli

Ingredients

• pound orecchiette
• tablespoons extra virgin olive oil, divided
• pound sweet or spicy Italian sausage, removed from casings
• garlic cloves, minced
• chicken broth
• pound broccoli florets
• teaspoon salt
• teaspoon red pepper flakes
• tablespoons unsalted butter
• freshly grated pecorino Romano