Special equipment: a 2-inch round cookie cutter
Preheat the oven to 375 degrees F. Coat a sheet pan with cooking spray.
Separate the biscuits and put them on the prepared sheet pan. Brush 8 of the biscuits with the heavy cream. Sprinkle all the biscuits with the Cheddar, then the chives. Put each biscuit brushed with cream on top of an unbrushed biscuit to make 8 biscuit stacks. Space the stacks evenly on the sheet pan. Cut out the center of each stack with a 2-inch round cookie cutter. Put the cut-outs in the empty spaces on the sheet pan.
Push a slice of ham down into each hole to make a cup that is deep enough to hold an egg comfortably. Crack 1 egg into each of the ham cups and sprinkle with the paprika.
Bake until the biscuits are flaky and golden brown, the egg whites are just set and the yolks are still jiggly when you lightly shake the sheet pan, about 20 minutes.
Serve each egg-in-a-hole with one of the biscuit cut-outs for dipping.
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