Bring a large pot of salted water to a rolling boil. Add the pasta and cook according to package directions until al dente, about 8-10 minutes.

About 2 minutes before the pasta is done, add the broccoli florets to the pot to blanch them until tender-crisp. Drain the pasta and broccoli, reserving ½ cup of the starchy pasta water. Set aside.

While the pasta cooks, melt the butter in a large skillet or Dutch oven over medium heat. Add the minced garlic and sauté for 30 seconds until fragrant.

Pour in the chicken broth and simmer for 1 minute, scraping up any browned bits. Stir in the heavy cream and reduce heat to medium-low.

Once the cream bubbles gently around the edges, reduce heat to low and slowly add the cheddar and Parmesan cheeses, stirring until melted and smooth. Season with salt and pepper. If too thick, add a splash of reserved pasta water.

Fold in the shredded rotisserie chicken and the drained pasta and broccoli. Stir until everything is heated through and coated in sauce.

Serve immediately, garnished with optional Parmesan, parsley, lemon juice, or paprika.