Mix together the butter and fresh herbs. Season with freshly ground black pepper. Place mixture on plastic wrap or wax paper and roll into a log shape of approximately 1-inch diameter and place in freezer. For the best results, do this the night before.
Preheat oven to 350 degrees F. In a large heavy-bottomed skillet, heat the oil to 300 degrees F or until a bread crumb sizzles when dropped in. DO NOT ALLOW OIL TO SMOKE!
Take chicken breasts and using a sharp knife, make a pocket on the top of the breast at least 1-inch long and about 1-inch deep. Remove butter from freezer and slice into disks about 1-inch long. Stuff the butter into the pocket made on the chicken breast, making sure the flap can close to hide the butter.
In preparation for breading, prepare the following: Season the flour with salt and pepper and place in a shallow dish. Mix the eggs and milk and place in another shallow dish. Place the bread crumbs in a third shallow dish.
Cover 1 chicken breast in flour, removing any excess. Then into the egg mixture, covering completely and removing any excess liquid. Then cover with breadcrumbs and place in hot oil. Cook until golden brown on outside and remove from oil. Repeat process with remaining chicken breasts. Drain and place on baking tray and put into the oven for another 10 to 12 minutes or until chicken is cooked through. Serve with crispy salad or vegetables and starch.