Heat oven to 450°. Combine the flour, 1 cup Parmesan, baking powder, sugar, pepper, and salt in a large bowl. Add the buttermilk, butter, tomatoes, and rosemary and stir until just combined.
Spoon two tablespoons of the dough into 1½ nonstick muffin pans (about 36 cavities, total). Sprinkle the tops with the remaining Parmesan cheese. Bake the biscuits until lightly golden and set, about 10 minutes. Let cool slightly in the pan, then transfer to a serving platter and top each muffin with a piece of folded prosciutto. Serve at room temperature.