1. Preheat oven to 350 degrees. Brush a 24-cup mini muffin pan with 1 tablespoon butter; set aside.

2. Stack two slices of bread on a work surface; using a rolling pin, flatten to an 1/8-inch thickness. With a 2-inch round cutter, cut two rounds from stack; separate to yield 4 bread rounds. Repeat with remaining bread to make 24.

3. Fit rounds into prepared muffin cups, gently pushing down in the center and being careful not to tear. Brush bread with remaining tablespoon butter. Bake until golden brown, 20 to 25 minutes. Cool in pan to room temperature. Leave oven on.

4. Meanwhile, in a medium bowl, stir together egg, ham, cheddar, cream, 1/8 teaspoon salt, and 1/4 teaspoon pepper. Carefully spoon 1 teaspoon of egg mixture into each bread cup. Bake until filling is set, 13 to 15 minutes.