In the same skillet, melt butter over medium heat.
Add garlic and sauté until fragrant, about 1-2 minutes.
Pour in heavy cream and chicken broth, stirring gently.
Bring the mixture to a simmer, then add grated Parmesan cheese.
Stir until the cheese is melted and the sauce has thickened slightly.
Top with broccolini and let cook in sauce.
Pour over the pasta and top with chicken.
Season with salt and pepper to taste.