In the bowl of a food processor, combine the flour, salt, pepper, paprika, and rosemary. Add the butter and grated cheese and toss lightly until coated in the flour mixture. Pulse in short bursts until the butter is the size of small peas.

Add the mashed sweet potato and pulse until combined. With the food processor running, add the milk. After a few moments, the dough will come together in a ball. Shape into a disk and wrap in plastic wrap. Chill for 30 minutes.

Preheat oven to 350 degrees. Line a sheet pan with parchment paper.

On a lightly floured surface, roll out the dough to about 1/4 inch thick. If the dough becomes sticky, add more flour. Cut the dough into 1-inch squares and transfer to the prepared sheet pan.

Use a toothpick to poke a hole into the center of each square. Sprinkle with the coarse salt and bake until the edges are just starting to turn brown, about 12-15 minutes.

Let cool, then store in an airtight container. Crackers are most crisp fresh from the oven.