Stir the relish, mustard, chives and honey together in a small bowl.
Cut the apple off its core and thinly slice into half-moons. Toss the apples with the lemon juice to keep them from browning.
Spread the rolls on both sides with the relish mixture. Build sandwiches with the Cheddar, apples, ham and arugula.
Recipe courtesy of Valerie Bertinelli