Step 1

Position an oven rack in the center of the oven and preheat to 425 degrees F.

Step 2

Pulse together the flour, baking powder, sugar and 1 1/2 teaspoons each salt and pepper in a food processor. Add the butter and pulse until pea-sized pieces form. Add the cheese and chives and pulse until just combined. Add the buttermilk and pulse a couple of times until the dough just comes together but is not fully incorporated.

Step 3

Turn the dough out onto a lightly floured surface and pat together gently into a ball. Use your hands to divide the dough into 6 even pieces. Generously coat a large baking sheet with cooking spray.

Step 4

Using the baking sheet as your work surface, pat each piece of dough into a 3 1/2-inch round about 3/4 inch thick. Arrange 3 dough rounds along the top long edge of the baking sheet, spacing them out evenly and making sure there is a 1/2-inch space between the dough rounds and the edges of the baking sheet. Arrange the remaining 3 dough rounds in the same fashion along the bottom long edge of the baking sheet. Cut the center out of each round with a 2-inch round cookie cutter. Arrange these smaller rounds evenly across the middle of the baking sheet.

Step 5

Brush the tops of all the dough pieces with buttermilk and bake until the smaller biscuits are golden, 12 to 15 minutes. Remove them and transfer to a plate.

Step 6

Lay a piece of ham over each of the large rounds. Push each ham piece down into the hole so that it forms a cup. Crack 1 egg into each of the ham cups. If a little of the egg white spills over, it's okay. Sprinkle the eggs with salt and pepper. Bake, rotating the pan front to back after 5 minutes, until the whites are just set and the yolks are still jiggly when you lightly shake the baking sheet, 8 to 12 minutes more.

Step 7

Use a spatula to remove them to individual plates and top each with a smaller biscuit piece for dipping into the egg.