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Light a fire well over to one side of your grill, using enough coals to fill a shoebox. When coals are all ignited, the flames have died down, and the temperature is hot (you can hold your hand 5 inches above the grill rack directly over the coals for 1 to 2 seconds), you’re ready to cook.
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Put butter, wine, garlic, and smoked paprika in a shallow foil pan large enough to hold clams in 1 layer and sturdy enough to resist the heat of the fire (do not add clams yet). Place pan on grill near fire, not directly over it, and cook, stirring a few times, until butter is melted and mixture is fragrant, 3 to 5 minutes. Let the sauce come to a simmer, then slide the pan to the side of the grill farthest away from the fire.
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Place clams flat on hot side of grill, directly on grill grate and cook until they pop open, 3 to 7 minutes. Use tongs to transfer clams, with any juices, to the pan containing the sauce as they are done. (Discard any that do not open.)
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While clams cook, arrange bread slices around the perimeter of the fire until lightly toasted, about 1 minute per side.
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When all the clams are in the pan, stir them around a bit to coat with sauce and sprinkle generously with parsley and kosher salt and pepper to taste.
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Serve clams right out of the pan, along with the toasted bread to soak up the juices.