In a bowl, beat together the softened butter, garlic, salt, cayenne pepper and parsley until well combined. Spoon the butter into a piping bag fitted with a large plain nozzle. Alternatively, put the butter into a food bag, twist the bag to push the butter into one corner and snip off the tip.
Using a sharp knife, make a deep, wide 'pocket' in the thickest end of each chicken breast, without cutting all the way through. Fill each chicken breast with as much of the butter mixture as possible.
Sprinkle the flour onto a plate. Beat the eggs in a bowl. Break up the panko breadcrumbs using your hands or pulse in a food processor. Sprinkle the crumbs onto another plate.
One by one, dust the chicken breasts first in the flour, then dip them into the egg, then roll them in the breadcrumbs until completely coated. Place the coated chicken breasts onto a plate, cover, then chill in the fridge for at least 20 minutes, or until needed.
When the chicken breasts have chilled, preheat the oven to 200C/400F/Gas 6.
Heat a little of the vegetable oil over a low-medium heat in a large non-stick frying pan. Fry the chicken Kievs for 3-4 minutes on each side, or until golden-brown all over. Sprinkle with salt flakes, then transfer to a roasting tray and cook in the oven for 10-15 minutes, or until the chicken is cooked through. (The chicken is cooked through when the juices run clear when the thickest part of the meat is pierced with a skewer - remember not to pierce the chicken all the way to the buttery centre!) Serve immediately.