Cook the pasta: Bring a large pot of salted water to a boil. Cook the pasta until just shy of al dente, 1 to 2 minutes less than package directions. Reserve 1/2 cup pasta water, then drain and set aside.

Prep the broccoli: If using fresh broccoli, cut into small florets. For a tender-crisp bite, blanch in the pasta water during the last 2 minutes of boiling, then drain. If using frozen, thaw briefly in warm water and pat dry.

Season the chicken: Pat the chicken dry. Season with 1 teaspoon salt, 1/2 teaspoon black pepper, and 1 teaspoon Italian seasoning. Toss to coat.

Sear the chicken: Heat 1 tablespoon olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Add chicken in a single layer. Cook 4 to 6 minutes, stirring once or twice, until browned and cooked through. Transfer to a plate and tent loosely with foil.

Sauté the aromatics: Reduce heat to medium. Add 2 tablespoons butter to the skillet. Stir in the minced garlic and cook 30 to 60 seconds until fragrant, not browned.

Build the sauce: Pour in the chicken broth and scrape up any browned bits. Stir in the heavy cream. Bring to a gentle simmer and cook 2 to 3 minutes until slightly thickened.

Add the cheeses: Reduce heat to low. Stir in the Parmesan a handful at a time until melted and smooth. If using cream cheese, add now and whisk until fully incorporated. Season to taste with salt and pepper. Add a pinch of red pepper flakes if you like a little heat.

Combine everything: Return the chicken to the skillet along with the cooked pasta and broccoli. Toss gently to coat in the sauce. If the sauce is too thick, loosen with a splash of reserved pasta water until it reaches a silky consistency.

Brighten it up: Add the zest of half a lemon and a small squeeze of juice. Taste and adjust seasoning. The lemon keeps the sauce lively without overpowering it.

Finish and serve: Sprinkle with chopped parsley and a bit more Parmesan. Serve warm straight from the skillet.