Trim the chicken breasts of any large clumps of fat that may be still attached. Slice a pocket into each breast. Be sure not to cut all the way through the meat, but rather just into one side, so that the fillings will stay in.

Stuff each piece of chicken with a slice of cheese and about four slices of pepperoni. Using a small skewer or 2 to 3 toothpicks, close up the pocket. Lightly season each piece with salt and pepper. Set the stuffed chicken aside.

Preheat your oven to 350°F and line a baking sheet with aluminum foil. Begin to heat a large skillet with 6 tablespoons of vegetable oil over medium-high heat. Collect three shallow dishes and put the flour in one, the egg in another, and the bread crumbs in the third. Beat the egg until it is an even consistency.

Coat each piece of chicken in the flour, then the egg, and then the bread crumbs. The flour helps the egg adhere, and the egg keeps the bread crumbs in place.