Bring a large pot of salted water to a boil. Add the uncooked orecchiette pasta and cook according to package instructions until al dente, about 8-10 minutes. Reserve about 1 cup of pasta water, drain the pasta in a colander, and set aside.
In a large skillet, heat 1 tablespoon of olive oil over medium heat. Add the Italian chicken sausage and break it into smaller pieces as it cooks. Sauté until browned and fully cooked, about 5-7 minutes.
Once the sausage is browned, add the smashed and chopped garlic to the skillet and sauté for about 1 minute until fragrant. Then, add the fresh broccoli florets, drizzle with the remaining tablespoon of olive oil, season with kosher salt and fresh cracked pepper, and stir well. Cook for an additional 3-5 minutes until the broccoli is bright green and tender.
Add the cooked orecchiette pasta to the skillet with the sausage and broccoli. Toss everything together gently, adding a splash of the reserved pasta water if the mixture seems dry.
Remove from heat and sprinkle the grated Pecorino Romano or Parmesan cheese over the pasta. Toss to combine, allowing the cheese to melt slightly and coat the pasta.
Serve immediately, garnished with additional cheese and freshly cracked pepper if desired.
