Cook pasta and broccoli: In a large pot with generously salted water, cook the pasta according to package directions. 3 to 4 minutes before the pasta cook time is up, add the broccoli florets and cook together with the pasta, until the pasta is al dente and the broccoli is tender crisp. Reserve 1 to 2 cups of pasta water for later just in case. Drain and run through cold water to stop the cooking process and to keep the broccoli crisp and bright green.
Season chicken with a few drizzles of olive oil, Italian seasoning, garlic powder, Kosher salt (1 teaspoon) and pepper.
In a skillet, melt 1 tablespoon of butter and cook the chicken until golden brown and fully cooked through. Transfer to a plate and set aside.
In the same skillet, melt the remaining 2 tablespoons of butter, and sauté garlic and shallots for a few seconds. Add the wine wine (or broth) to deglaze, scraping the brown bits to release.
Stir in the half-and half and bring to a light simmer for a few seconds. Then, add the cooked pasta and some of the reserved pasta water as needed. The pasta water will help thicken the sauce, which should be light and slightly creamy. Season with salt and pepper to taste.
Return the cooked chicken and broccoli to the skillet, and toss until coated. If needed, add more half-and-half and pasta water until you get the right consistency.
Finish with grated parmesan cheese tossing to combine.
To serve, top with fresh lemon zest and more parmesan cheese as garnish. Enjoy!