If you like the concept but aren't into broccoli try my other stuffed chicken breast dish Chicken Roulades.
Shelly's Broccoli and Cheese Stuffed Chicken Breast
4 boneless skinless Chicken Breasts, pounded thin
1/2 yellow Onion, diced
2 green Onions, diced
1 cup Broccoli, cooked chopped
Kosher Salt and freshly ground Pepper, to taste
1/2 teaspoon Greek Seasoning
4- 1 oz chunks of Swiss Cheese
1 Egg, beaten
3/4 cup Parmesan cheese, grated
Olive oil
Butter
Pound chicken breasts to about 1/3" thick. Saute onions in oil/butter. Add to cooked broccoli. Add seasonings. Mix. Place spoon of broccoli mixture on chicken and top with a chunk of swiss cheese. Roll up; securing with a toothpick. Dip each breast-roll in beaten egg. Roll in Parmesan cheese and place in a pyrex baking dish. Bake at 350 for 30 minutes covered, 10 minutes uncovered or until slightly browned and cooked through.