In a small bowl, mix together the butter, garlic, parsley, salt and pepper. Gather the butter mixture and roll into a six inch-long log. Wrap in plastic wrap and chill for one hour, until it is firm.

Cut the butter log into 12 equal pieces and roll each into a one inch-long log. Chill the butter logs for 30 minutes, until they are firm.

On a work surface, season the flounder fillet halves with salt and pepper. Beginning with the narrow end, roll up each fillet around a butter log and secure each roll – including the sides – with wooden picks to enclose the butter completely.

Place the flour in a shallow bowl. Beat the eggs with the milk in a small bowl.

Place the bread crumbs into another shallow bowl. Dredge each flounder roll in the flour, shaking off the excess. Dip it into the egg mixture and let the excess drip off, then dredge it in the bread crumbs, making sure the fish roll is coated completely and evenly. Transfer the fish rolls as they are coated to a paper-lined baking sheet and chill them, covered, for one hour. Remove toothpicks.

In a heavy stockpot, heat two cups oil to 375°F on a deep-fry thermometer. Once the oil has reached the proper temperature, fry the fish rolls in batches, turning them carefully, for seven to 10 minutes, or until the fish is cooked through and the coating is crisp. Transfer them with a slotted spoon to paper towels to drain. Serve immediately.