Prepare the garlic butter: In a bowl, mix softened butter, minced garlic, chopped parsley, lemon juice, salt, and black pepper until smooth. Shape into a log, wrap in plastic wrap, and freeze for 15-20 minutes until firm.
Prepare the chicken: Using a sharp knife, carefully cut a pocket in each chicken breast without slicing all the way through.
Stuff the chicken: Slice the chilled butter log into pieces and place a piece inside each chicken pocket. Secure the opening with toothpicks if necessary.
Coat the chicken: Dredge each stuffed chicken breast in flour, dip in the beaten eggs, and coat thoroughly with breadcrumbs.
Chill: Refrigerate the breaded chicken for 15 minutes to help the coating set.
Fry the chicken: Heat vegetable oil in a deep skillet over medium heat. Fry the chicken for 4-5 minutes per side until golden brown.
Bake (optional for thorough cooking): Transfer the fried chicken to a preheated oven at 350°F (175°C) and bake for 10-12 minutes to ensure the chicken is fully cooked.
Rest and serve: Let the Chicken Kyiv rest for 5 minutes before slicing to allow the butter to stay inside. Enjoy!