Heat grill to low. Lay slices of bread on a clean work surface; spread with mustard, dividing evenly. To make four sandwiches, layer bread with ham, arugula, cheese, and onion, beginning and ending with cheese.
Place sandwiches on grill; cover grill, and cook until cheese melts, 4 to 5 minutes per side (shift position on grill if necessary to prevent charring).
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