Prepare the garlic herb butter by combining softened butter, minced garlic, parsley, dill (if using), lemon zest (if using), salt, and pepper. Mix until fully incorporated, then shape into a log using plastic wrap and refrigerate for at least 1 hour.

1. Prepare the chicken by pounding each breast between sheets of plastic wrap to an even thickness of 1/2-inch. Cut the chilled garlic herb butter into 4 portions. Place one portion in the center of each chicken breast, fold the sides over the butter, and roll tightly to seal. Secure with toothpicks.
2. Bread the chicken by dipping each stuffed chicken breast in flour, then in beaten eggs, and finally in breadcrumbs. Press gently to ensure the coating sticks well.
3. Heat vegetable oil in a skillet over medium-high heat. Fry the chicken for 4-5 minutes on each side, until golden brown and crispy. Drain on paper towels.
4. Remove toothpicks and serve immediately, garnished with extra parsley if desired. Serve with mashed potatoes or a fresh salad.