Mix the butter in a bowl with the garlic, lemon rind, tarragon and nutmeg. Season to taste with salt and pepper. Shape the butter into a rectangular block about 2-inch long, wrap in a foil and chill for 1 hour in the refrigerator
Place the chicken, skinned sides down, on a piece of oiled clear plastic wrap. Cover with a second of piece of plastic wrap. Gently beat the fillet pieces with a rolling pin until fairly thin, about 1/8-inch thick
Cut the butter lenghtways into four pieces and put one in the center of each chicken fillet. Fold in end of chicken and roll into small logs, make sure it completely cover the butter
Tip the beaten egg and the bread crumbs into separate small dishes. Dip the chicken pieces first in the beaten egg and then in the breadcrumbs to coat evenly. Dip them a second time in egg and crumbs, then put on a plate and refrigerate for at least 1 hour or overnight
Heat the oil in a large pan or deep fat fryer to 350 F. Gently place each breast in oil, sealed-side down, and cook until golden brown, approximately 4 to 5 minutes on each side. Serve hot, garnished with lemon wedges if you like