Preheat the oven to 400F with one rack in upper third of the oven and the other in center of oven. Line two baking sheets with aluminum foil. In the first baking sheet, arrange the bacon slices in a single layer. Bake in oven in the center rack while you proceed with the next step.
In the other lined baking sheet, arrange the clams in a single layer. Place this in the upper third of the oven. Bake for 6-7 minutes, until the clams have opened. Larger, cherrystone clams will take a little longer. Carefully remove the baking sheet with the clams (be careful, there may be juices in the pan) to a large bowl, along with the juices to let cool. You can return any unopened clams back to the oven for another minute or so, to see if they open. Discard any unopened clams after that.
Arrange a big spoonful rock salt on the still-lined baking sheet in 24 small piles, one for each clam. When the clams are cool enough to handle, pry open and discard the top shell. Collect the clam juices as you go in a medium bowl.
Use a paring knife or small spoon to loosen the clam from the bottom of the shell. This will make it easier to eat.
Place the clam onto the rock salt bed, snuggling it in, so that the rock salt stabilizes the clam. Repeat with remaining clams.
To the reserved clam juice bowl (double check for any shell bits), mix in the melted butter, wine, parsley and garlic.
Season with salt and pepper, to taste (also, remember you have salty bacon and Parmesan to add as well). At this point, I like to check on the bacon, to make sure it's crisping up nicely. If the bacon looks done, go ahead and remove it.
Spoon a little of the butter mixture into each clam half. Top each clam half with the grated Parmesan cheese. Bake the clams in the upper rack for 5 minutes, until the butter is bubbling a bit. The bacon should be perfectly cooked at this time, too. Remove the clams and the bacon from the oven.
Cut the bacon into 24 pieces, top each clam with the bacon. Serve with lemon wedges.