In a bowl, mix together the butter, shallot, garlic, parsley, wine, salt and pepper until thoroughly combined. Lay out a large piece of plastic wrap over a work surface and mound the butter in the center. Fold the plastic wrap over the butter and shape into a rough log shape. Transfer to the refrigerator and chill until firm, at least 2 hours.
Turn your oven broiler to medium-high heat.
Rinse your oysters in cold water and discard any open ones. Using a heavy duty tea towel, hold the oyster firmly in one hand with the flat shell side facing up. Using your other hand, insert an oyster shucking knife into the hinge of the oyster, easing it in where you can. Make sure your hand holding the oyster is well protected by the towel. Once you feel the knife is firmly anchored in the hinge of the shells, twist the knife to pop open the oyster.
Clean your knife and then slide it along the top shell to release the muscle from the shell. Remove the top shell and discard. Lastly, run the knife under the oyster so that it is resting in the bottom shell, but no longer connected to it. (This ensures that it will easily slide into your mouth when eaten). Any oysters that have an unpleasant odor should be discarded.
Cover an oven-safe serving dish with a layer of rock salt. Arrange the oysters over top, nestling the shells into the salt so they won’t slide around when grilling. Top each oyster with a slice of the cold butter. Place in your oven and broil for 5-7 minutes. When the butter has melted, is golden and you can see it bubbling at the edges, your oysters are ready.
Serve immediately with some crusty bread to soak up any leftover sauce.
If you have any leftover butter, this is great used as a topping on beef or, of course, escargot!