1. Combine butter, dill (or parsley), garlic powder, salt and pepper. Place the mixture on plastic wrap and roll into a small log. Place in freezer.
2. Using a sharp knife, slice halfway through the thickness of each chicken breast, cutting it almost all the way through. Stop cutting when you reach about 1/2 inch from the end of the breast and open it like a book. Place chicken breasts, 1 at a time, between 2 pieces of plastic wrap. Even out the chicken breast's thickness by pounding it carefully (until about 1/5 inch thick). Season each piece of chicken with salt and pepper.
3. Remove the butter mixture from freezer (it should be firm) and divide into 3 equal pieces. Place one piece of butter on each chicken breast. Fold in edges of chicken and then roll to encase the butter completely. Place in freezer for about 10 minutes.
4. In a medium size deep frying pan, heat oil to medium-high.
5. Beat eggs with a fork or a whisk. Dip each breast in the eggs and then roll in the bread crumbs, then dip in the eggs again and coat evenly with bread crumbs.
6. Gently place each breast in oil, sealed-side down, and cook until golden brown, approximately 5-7 minutes on each side. Drain on paper towels and serve.
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