For the salad: Drain the Corn Relish and pulse to chop in a food processor. Mix the relish, ham, celery and mayonnaise until well blended, and then season with salt and pepper.
For the sandwich: Place 6 ounces of the salad on each bun. Top with a generous amount of arugula, and then serve immediately.
Heat the oil in a large pan. Saute the onions and peppers until the onions are translucent. Add in the vinegar to deglaze, stirring to get all the good bits from the bottom of the pan. Add in the sugar and salt, and stir until dissolved. Continue cooking until the vinegar reduces by one-quarter.
Stir in the corn until fully incorporated. Remove from the heat, and add in the thyme and black pepper. Cool before serving.