Step 1

In a large microwave-safe bowl, combine the salami and prosciutto. Microwave on high, uncovered, until the meats just begin to crisp, about 1 minute, stirring once halfway through. Pour off and discard any fat in the bowl; cool to room temperature.

Step 2

Line 2 rimmed baking sheets with kitchen parchment. In a food processor, combine the flour, yeast and pepper; pulse until well combined, about 12 pulses. Scatter in the butter, then pulse until the mixture resembles coarse sand, 10 to 12 pulses. Empty the mixture into the large bowl containing the meats, then add the provolone. Using a silicone spatula, fold until the ingredients are evenly distributed. Drizzle the water over the mixture, then fold with the spatula until the mixture comes together in a cohesive, evenly moistened dough.

Step 3

Using a ½-cup dry measuring cup, scoop the dough into 12 even portions, lightly packing the dough into the cup and placing 6 on each prepared baking sheet, evenly spaced; the dough should easily invert out of the cup in a puck-like shape. Cover each baking sheet with a kitchen towel and let rise at room temperature for 1 hour.

Step 4

Meanwhile, heat the oven to 425°F with a rack in the middle position. Uncover 1 baking sheet and bake until the buns are golden brown, 25 to 27 minutes. Remove from the oven and, using a wide metal spatula, transfer the buns to a wire rack. Bake the second batch in the same way. Cool to room temperature.