Cook orecchiette pasta according to package directions and reserve 1 1/2 cups pasta water. Then drain pasta and set aside.
In a large skillet or pot, heat 3 tbsp olive oil over medium heat. Once warm, add shallots and sauté 2-3 minutes until starting to soften.
Add minced garlic and red pepper / chili flakes and sauté 2-3 more minutes.
Then, add sausage (that's been removed from the casing) and cook for 8-10 minutes until done, breaking into smaller pieces as it cooks.
Stir in broccoli with a pinch of pepper, 1/4 tsp salt and 1/2 cup pasta water. Cook until broccoli is tender about 7-10 minutes.
Finally, stir in the cooked orecchiette pasta and the rest of the pasta water, cooking for 2 more minutes. Remove from the heat and stir in 1/2 cup of parmesan cheese. Serve with remaining parmesan cheese.
Notes
And don't fret if you forget to reserve the pasta water, chicken broth works well too.