In a large pot, bring salted water to a boil. Add the ziti pasta and cook until al dente, about 8-10 minutes. In the last 3-4 minutes, add the broccoli florets, allowing them to steam until bright green. Drain the pasta and broccoli together, then rinse under cold water.

While the pasta is cooking, season the chicken breasts with olive oil, Italian seasoning, garlic powder, salt, and pepper. In a large skillet, melt 1 tablespoon of butter over medium heat. Cook the chicken for about 6-7 minutes on each side, or until golden and cooked through. Remove the chicken from the skillet and set aside.

In the same skillet, melt the remaining 2 tablespoons of butter over medium heat. Add minced garlic and shallots, sautéing for about 1 minute. Pour in the white wine, scraping up any browned bits. Let it simmer for 2-3 minutes until slightly reduced, then stir in the half-and-half.

Add the cooked ziti and reserved pasta water until the desired creaminess is achieved. Return the chicken and broccoli to the skillet, gently tossing everything together. Cook for an additional minute to heat through and meld the flavors.

Remove from heat and stir in the Parmesan cheese until melted. Top with lemon zest and additional Parmesan if desired. Serve warm.