Melt 2 tablespoons butter in a large skillet. Add red onions and cook until soft. Stir in brussel sprouts and cayenne pepper and cook for an additional 5 minutes. Remove from heat. Season with salt and pepper to taste.
Cut chicken breasts in half horizontally, leaving 1 long side attached by about ½ an inch. Open the chicken breasts like you would a book.
Place plastic wrap on top of the chicken and pound breasts until they are about ¼ to ½ inch thick. Remove plastic and season both sides with Kosher salt and pepper.
With the cut side facing up, scoop ⅓ or ¼ of the vegetable mixture (depending on how many total chicken breasts you are using) into the center of each piece of chicken, leaving about a ½ inch border from the ends. Sprinkle with about 2 ounces of feta.
Roll chicken lengthwise (against the line of the cut you made) and tie off with kitchen twine.
Melt remaining 3 tablespoons of butter in skillet. Add stuffed chicken and cook on for 5-8 minutes on each side until nicely browned. Transfer chicken to a baking dish and bake for 10-12 minutes.
Remove from oven and let rest for 10 minutes. Remove twine and slice into 1-2 inch thick pieces.