Heat 2 Tbsp butter in a large heavy skillet over medium heat until foam subsides. Stir in leeks and season with salt. Reduce heat to low and cook leeks, covered, stirring occasionally, until tender, about 10 minutes. Remove from heat and keep warm.
Puree remaining 4 Tbsp butter with garlic, parsley, and snails. Season with salt and pepper.
Put scallops in gratin dishes. Season with salt and pepper, then dot each with 1 tsp snail/garlic butter.
Bake in the middle of the oven until scallops are just cooked through, about 9 minutes.
Serve topped with leeks and sprinkle with chives and remaining parsley.