Bring a large pot of salted water to a boil and add ziti pasta. Cook until al dente, about 8-10 minutes. Add broccoli for the last 3-4 minutes. Refresh in cold water and drain, reserving about a cup of pasta water for later.

Season chicken breasts with salt and pepper. Heat olive oil in a skillet over medium-high heat. Cook chicken for 6-7 minutes on each side until golden brown and cooked through. Remove and let it rest before slicing.

Lower heat and add butter to the same skillet. Once melted, stir in minced garlic and shallots, cooking for 2-3 minutes until fragrant. Deglaze with white wine or broth, scraping up browned bits.

After reducing the liquid slightly, stir in half-and-half and simmer for 3-5 minutes until thickened. Gradually add reserved pasta water to reach desired sauce consistency.

Introduce cooked ziti, broccoli, and sliced chicken back to the skillet. Add Parmesan cheese and toss gently to coat. Adjust salt and pepper to taste.

Sprinkle lemon zest over the top and serve warm, garnished with additional Parmesan if desired.