Step 1

Preheat oven to 450°F. Line a baking sheet with parchment paper. Whisk together flour, baking powder, baking soda, salt, and sugar in a bowl. Add butter and cut in with a pastry blender or two forks until butter is the size of small peas. Stir in chives and 4 ounces Cheddar. Make a well in the center; add buttermilk and stir until just combined.

Step 2

On a lightly floured work surface, roll or pat dough into a 1/2-inch-thick rectangle. Fold dough edges into center, like folding a letter into thirds. Roll or pat dough to a 1/2-inch-thick rectangle, and repeat folding process. Cut dough into 6 pieces; press each piece into a 3 3/4-inch round (about 1 inch thick). Place dough on prepared baking sheet. Cut out center of each dough round with a 2-inch round cutter. Place dough centers around the larger dough rounds in middle of baking sheet. Freeze at least 15 minutes and up to 2 hours.

Step 3

Meanwhile, line a second rimmed baking sheet with parchment paper. Arrange bacon in a single layer on prepared baking sheet. Bake until fat is beginning to render and edges are curled and lightly browned, 8 to 10 minutes. (Bacon will not be crisp.) Transfer bacon to a paper towel-lined plate.

Step 4

Place baking sheet with frozen biscuits inside another baking sheet of the same size. (This will insulate the tray so that the bottoms do not over-brown.) Bake until small biscuits are golden brown, 12 to 15 minutes. Transfer small biscuits to a plate.

Step 5

Place 2 bacon strips into center hole of each large biscuit. Sprinkle remaining 2 ounces Cheddar over bacon, dividing evenly, pressing to create a well in the middle of cheese. Crack 1 egg into each well. Sprinkle with salt and pepper. Bake, rotating sheet halfway through, until egg whites are just set, 12 to 15 minutes. Serve each egg in a hole with a small biscuit and garnish with chives.