To make the alfredo sauce, in a nonstick frying pan over medium heat melt the butter and warm the olive oil and stir in the heavy cream and parmesan cheese.
When the sauce will be slightly thickened stir in the broccoli florets and season with salt and pepper to taste.
Cut the chicken breasts in the center and fill each breast with broccoli filling.
Season the top with salt and pepper and add some cheese on top.
Transfer to a baking tray lined with a piece of parchment paper and sprinkle grated cheese on top.
Bake in an already heated oven at 350 F or 180 C degrees for about 35-40 minutes.