Heat oven to 425 degrees. Place clams in a large pot with water. Cover and cook over high heat until clams open, about 10 minutes. Remove from shells, there should be about 1 cup of clams. Reserve 24 shells for stuffing (you may not need all 24).
Process clams briefly in a food processor. Do not overprocess or the clams will become liquid. You could also finely chop the clams by hand.
Combine clams, butter, shallots, garlic, parsley, basil, bread crumbs, 6 tablespoons cheese, wine, prosciutto, pepper flakes, and salt and pepper to taste in a bowl. Stuff shells with mixture and smooth top. Sprinkle remaining parmesan over top of clams and arrange them in a shallow baking dish. Sprinkle with olive oil.
Place in oven and bake for 15 minutes. Run clams under broiler briefly for a final glaze.