Step 1

Preheat the oven to 425 degrees F and line a rimmed baking sheet with parchment.

Step 2

Pulse the flour, baking powder, sugar and salt in a food processor until combined. Add the butter and 1/2 cup of the Cheddar and pulse until the mixture looks like coarse meal with pea-size bits of butter remaining. Add the buttermilk and pulse a few times, until the dough just comes together.

Step 3

Turn the dough out onto a work surface that’s lightly dusted with flour, then pat into a 7-by-7-inch square that's about 1 inch thick. Scatter half of the ham and 1/4 cup of the Cheddar on half of the dough, then fold the other half of dough over like a book; gently pinch the edges to seal. Pat the dough out again into a 7-by-7-inch square, scatter the remaining ham and 1/4 cup of cheese on top and fold the dough over like a book. Press once more into a 7-by-7-inch square.

Step 4

Use a sharp chef’s knife to cut the dough into 12 even rectangular pieces. Transfer to the prepared baking sheet and brush the tops of each piece with additional buttermilk. Bake until the biscuits are puffed and well browned, 18 to 20 minutes.