Crank the oven to 425°F (218°C). Line a baking sheet with parchment paper or a nonstick Silpat pad.
In a large bowl, stir together the flour, baking powder, sugar, salt, and cayenne.
Using a fork, stir the grated butter into the flour mixture.
Stir in the ham, scallions, and cheese.
Pour in the buttermilk and gently fold it in the flour mixture until evenly moistened. If the dough is has dry spots, drizzle in a little additional buttermilk, 1 tablespoon at a time, until the dough is moist but not wet. Don’t overwork the dough!
Turn the dough out onto a lightly floured surface and gingerly pat the dough into an 8-by-10-inch (20-by-25-cm) rectangle about 3/4 inch (18 mm) thick.
Dip a 3-inch (8-cm) biscuit cutter into flour and cut as many biscuits as you can from the dough, pressing straight down with the cutter each time. (Don’t twist while cutting or the biscuits won’t rise evenly.)
Gently press together the scraps and cut more biscuits, repeating until all the dough is used.
Place the biscuits on the prepared baking sheet and bake, turning the pan halfway through, until light golden brown, 15 to 25 minutes.
Transfer the biscuits to a wire rack and immediately brush the tops with the melted butter.
Serve warm. (The biscuits will keep, wrapped in plastic, at room temperature for up to a day, or in the freezer for up to 4 months. Gently rewarm in a low oven or the microwave before serving.)