Mix together the butter, garlic, parsley, lemon juice and rind. Spoon onto a sheet of foil and shape into a rectangle about 2x3 inches. Roll up the foil and chill until firm.
Place each piece of chicken between 2 sheets of plastic wrap and use a meat mallet or rolling pin to gently flatten to about 1/4 inch thickness.
Cut the chilled butter into 6 pieces. Place a piece in the center of each chicken slice, fold in the edges and roll up to completely enclose. Fasten with toothpicks and chill until firm.
Place the flour and breadcrumbs on separate plates or greaseproof paper. Toss the chicken in the flour, dip in the combined egg and milk, then coat with the breadcrumbs. Chill on a paper-lined tray in the fridge for 1 hour, then toss in the egg and breadcrumbs again. Half fill a heavy-based frying pan with oil and cook the chicken, in batches, for 5 minutes on each side, or until golden and cooked through. Drain on paper towels, remove the toothpicks and serve with the lemon wedges.
Note: Prep time listed does not include 2 hours of refrigeration time.