Divide the turkey into 4-6 pieces and roughly press into patties, without being particularly careful about shaping them—a rough edge will create more crispy bits.
Heat a large, heavy skillet or griddle until it’s very hot, add a drizzle of oil and cook the patties, pressing down on them with a spatula or potato masher to flatten to slightly larger than the buns you plan to use—because it’s so lean, there will be little shrinkage. Sprinkle with salt and pepper as you cook the burgers for 4-5 minutes, until they’ve developed a nice bottom crust.
Flip (use a thin spatula) and cook for a few minutes on the other side. Spoon some tomato sauce overtop, place a piece of provolone on the sauce, and sprinkle with Parmesan. Cover and cook for another minute, or until the cheese melts—alternatively, put all the patties onto a foil or parchment-lined baking sheet and slide into a hot oven for a few minutes to melt the cheese. (This is useful if you already have the oven on for fries.) Serve on soft buns, with mayo and lettuce if you like. Serves 4-6.