Using a 1 1/2-inch round cookie cutter, cut 36 rounds of brioche from slices. Place 1 tablespoon butter in a 12-inch skillet. Melt over medium heat. Add half the rounds; cook until golden, turning once, 1 to 2 minutes per side. Repeat with remaining butter and rounds. Let cool on a wire rack or paper towel. Store rounds in an airtight container at room temperature for up to 2 days.
Place a dollop of creme fraiche on each round, and top with caviar.