Combine the torn mozzarella, basil, parsley, minced garlic, Parmesan, red pepper flakes, salt, and pepper in a small bowl. Mix gently until all ingredients are distributed evenly throughout the cheese.

Remove the chicken breasts from their packaging and place them on a clean cutting board. Pat them thoroughly with paper towels to remove any surface moisture.

Place one chicken breast flat on the cutting board with the thickest side facing you. Using a sharp knife, carefully cut horizontally through the thickest part of the breast, moving from the thicker side toward the thinner edge, but stop before cutting all the way through. The chicken should open like a book. Repeat with all four chicken breasts.

Open each butterflied breast flat on the cutting board. Place plastic wrap or parchment paper over the chicken and gently pound it with a meat mallet or the bottom of a rolling pin until it's an even thickness of about 1/2 inch.

Divide the filling mixture equally among the four chicken breasts, spooning it onto one half of each opened breast. Fold the empty half over the filling side, creating a pocket shape. Press the edges together gently to seal them, using your fingers to crimp or pinch where the two pieces meet.

Sprinkle both sides of each stuffed chicken breast with salt and pepper to taste.

Heat the olive oil and butter together in a large skillet over medium-high heat. Once the butter foams and the oil shimmers, carefully place each stuffed chicken breast into the pan.

Sear the chicken for 6 to 7 minutes on the first side without moving it.

Flip each chicken breast carefully using tongs and sear the second side for another 5 to 6 minutes. The internal temperature should reach 165 degrees Fahrenheit when measured with an instant-read thermometer inserted into the thickest part of the meat, away from the filling.

Transfer the cooked chicken to a clean plate and let it rest for 3 to 5 minutes before serving or cutting into it.