Combine the cheese, mayonnaise, pimento, relish, pepper and salt in a medium bowl and stir until combined. Spread the cheese mixture on the cut sides of both the top and bottom bread halves of each sandwich. Divide the ham and onions evenly between the 4 sandwiches, sandwiching between cheese-slathered bread. Wrap sandwiches individually in foil and place on a plate or baking sheet. Apply weight from the top using a skillet or other heavy object and refrigerate (in this pressed fashion) for at least a few hours, preferably overnight.