Fry the ham in a medium skillet until nicely warmed; set aside.
Spread the pumpernickel slices with the mayonnaise.
Place 2 slices of bread, mayo-side down, in the hot skillet. Divide the ham, asparagus and Taleggio between the slices. Place a second slice of bread, mayo-side up, on top. Cook, pressing down with a spatula, until golden brown on one side; flip, and continue cooking until golden brown on the reverse side and the cheese is melted.