In a large mixing bowl, whisk together the butter, Worcestershire, lemon juice, parsley, garlic, and black pepper. Lay out plastic wrap and roll the butter on it into a 2-inch-thick log. If you are making the oysters within the next few hours, you can simply keep the butter covered at room temperature. Otherwise, refrigerate it; it will keep for a few days, and it’s great on toast or pasta. (In the freezer, it will keep for several months.)
Meanwhile, pour the kosher salt into a medium bowl and then add water 1 tbsp. at a time, mixing it together until the salt begins to clump and stick to the touch. Lay the salt mixture into a cast-iron skillet in an even layer.
Nestle shucked oysters on the half shell into the salt so that they are stable and sitting upright without spilling their liquor. If you are not cooking the oysters right away, keep the skillet in the refrigerator until it is needed (the same day is ideal).
When you are ready to cook the oysters, preheat the broiler to high and place one of the oven racks on the highest level.
Cut 12 ¼-inch slices of the garlic butter and place one piece atop each oyster, then top them very liberally with freshly grated Parmesan. Place the skillet under the broiler, rotating the skillet after about 1 minute. Broil the oysters until the butter and Parmesan are melted and the butter is sizzling around the sides of the shell—about 1 more minute. Note: You are not looking for the Parmesan to be browned.
Serve immediately, with lemon wedges.