Place 1 bread slice between 2 sheets of waxed paper; roll to 1/4-inch thickness. Cut off and discard crust. Repeat with remaining bread slices.
Spread bread slices with mayo and mustard mixture; top with a cheese slice, spread out 2 ounces of ham spread, then place the pickle spear on top of the ham at one end. Roll up, starting at the pickle side of each slice of bread.