Prepare the Chicken:
Lay the chicken breasts flat on a cutting board. Carefully, with a sharp knife held sideways, create a pocket in the center of each breast by slicing into the thicker part without cutting through the bottom or sides. Repeat with all the chicken breasts.
In a small bowl, mix together the minced sun-dried tomatoes, feta cheese, 3 tablespoons of pesto, and parsley until evenly combined.
Stuff the Chicken:
Season the inside of each chicken breast pocket with a sprinkle of salt and pepper.
Evenly distribute the tomato and feta mixture into the pocket of each chicken breast, pressing lightly to ensure even stuffing. Use a couple of toothpicks to secure the opening of each pocket.
Rub the outside of each chicken breast with some of the remaining pesto.
Cook the Chicken:
Preheat a large cooking pan over medium heat and add the olive oil.
Place the stuffed chicken breasts in the pan. Allow them to sear, then flip to cook the other side.
Cover the pan with a lid and reduce the heat to medium-low. Continue cooking, flipping the chicken halfway through to ensure even browning and cooking on both sides. Cook until the chicken is done and has reached an internal temperature of 165°F (75°C). This may take 20-30 minutes depending on the thickness of the chicken breasts.
Remove the lid during the last few minutes of cooking to let the chicken brown nicely.