Make the Butter Filling: Place softened butter in a bowl. Add garlic, lemon juice, parsley, dill, salt, and pepper. Mix until smooth and well blended. Spoon the mixture onto parchment paper and shape into a small log. Chill until firm so it stays inside the chicken.
Prepare the Chicken: Lay chicken breasts flat on a board. Carefully slice a pocket into the side of each breast without cutting through. Season inside and out with salt and pepper.
Fill and Seal: Cut chilled butter into pieces. Tuck one piece into each chicken pocket. Press edges together firmly to seal the butter inside. Chill the stuffed chicken briefly to help it hold shape.
Set Up Breading Station: Place flour in one bowl, beaten eggs in another, and breadcrumbs in a third. Coat each chicken breast first in flour, then egg, then breadcrumbs. Press gently so the coating sticks well.
Heat the Oil: Pour vegetable oil into a skillet. Heat over medium until hot but not smoking. The oil should sizzle gently when chicken touches it.
Fry the Chicken: Place chicken in the pan carefully. Cook until golden on all sides, turning gently. Keep the heat steady so the coating browns evenly.
Finish Cooking: Lower heat slightly and continue cooking until chicken feels firm and cooked through. Let the chicken rest a few minutes before slicing so the butter stays inside.
