Step 1: Heat olive oil in a large skillet or Dutch oven over medium-high heat. Add the sliced smoked sausage and cook until browned on both sides, about 5-7 minutes.
Step 2: Remove the sausage from the pan and set aside. In the same pan, add the diced onions and sauté until translucent, about 3 minutes. Add the garlic and red pepper flakes, cooking for another minute until fragrant.
Step 3: Pour in the chicken broth and bring to a simmer. Use a wooden spoon to scrape the browned bits from the bottom of the pan.
Step 4: Add the dry pasta to the simmering broth. Cover and cook for about 8-10 minutes, or until the pasta is nearly al dente, stirring occasionally to prevent sticking.
Step 5: Stir in the broccoli florets and the cooked sausage. Cover and cook for an additional 3-5 minutes until the broccoli is tender and the pasta is fully cooked.
Step 6: Remove from heat and stir in the Parmesan cheese until melted and a light sauce has formed. Season with salt and pepper to taste and serve immediately.