Combine first 4 ingredients in a bowl; stir well. Spread about 3 tablespoons cheese mixture onto each pumpernickel bread slice. Top each with a sourdough bread slice. Cut each sandwich into four squares. Arrange sandwiches on a serving platter, some pumpernickel side up and some sourdough side up.
Polka-Dot Sandwiches: To make sandwiches more artistic, cut 4 small circles from each pumpernickel slice and 4 small circles from each sourdough slice using a 3/4" to 1" biscuit cutter. Place the white sourdough circles in holes in pumpernickel. Place the brown pumpernickel circles in the holes n the sourdough slices. Assemble sandwiches as directed.