Heat 2 tablespoons of butter in a medium skillet over medium-high heat, add the celery and onion and cook for about 3 to 4 minutes. Add the garlic and cook for an additional minute.
In a bowl, combine the lump crab meat, panko, egg, celery, onion, garlic, thyme, and a pinch of Old Bay. Use your hands to make sure that the stuffing is fully mixed.
Heat an oven to 375 degrees.
Lay the flounder flat and put 1/4 of the stuffing in the center of each filet. Roll the flounder around the crab stuffing and place on a baking sheet with the ends of the fish, where it overlaps, facing down. Spread butter over the top of the fish and sprinkle with a pinch of Old Bay seasoning.
Cook the fish for 30 minutes or until thoroughly cooked. Serve with prepared hollandaise sauce and vegetable of your choice.