1. Remove all meat from rotisserie chicken and shred into bite-sized pieces. Discard skin and bones. Set aside.

2. Cut broccoli into small, bite-sized florets. Mince garlic and grate Parmesan cheese fresh from block.

3. Bring large pot of salted water to boil. Add pasta and cook according to package directions until al dente.

4. During the last 3 minutes of pasta cooking, add broccoli florets to the boiling water with the pasta.

5. Drain pasta and broccoli together, reserving 1 cup of pasta water. Set aside.

6. In the same pot, heat olive oil and butter over medium heat. Add minced garlic and optional red pepper flakes. Sauté for 1 minute until fragrant.

7. Pour in heavy cream, chicken broth, and milk. Bring to gentle simmer, stirring occasionally. Do not let it boil rapidly.

8. Reduce heat to low. Gradually stir in Parmesan and mozzarella, whisking constantly until melted and smooth.

9. Add Italian seasoning, onion powder, salt, and pepper to the sauce. Stir to combine.

10. Add drained pasta and broccoli to the sauce. Toss to coat evenly.

11. Fold in shredded chicken gently until combined and heated through.

12. If sauce is too thick, add reserved pasta water 1/4 cup at a time until desired consistency.

13. Taste and adjust seasoning. Stir in fresh parsley.

14. Serve immediately in warm bowls, topped with extra Parmesan, fresh parsley, and optional lemon wedges.