Melt the remaining 2 tablespoons butter in the same skillet. Add the onion and cook 5 to 8 minutes until softened.
Add the broccoli and cook 3 to 4 minutes until it just begins to soften.
Stir in the cream of chicken soup, heavy whipping cream, and 1 cup of the shredded cheddar until smooth and creamy.
Pour the sauce evenly over the chicken.
Bake uncovered for 40 minutes.
Sprinkle the remaining 1 cup cheddar over the top and bake 5 to 10 minutes more, until the cheese is melted and bubbly and the chicken reaches 165°F.
Rest 5 to 10 minutes before serving. Spoon extra sauce over each portion.