Crusty ciabatta rolls stand up well to the ingredients in these sandwiches and won't get soggy in your picnic basket. If you can't find ciabatta, substitute another crusty roll or baguette. If you prefer to use softer rolls, pack the dressing separately and add it to the sandwiches just before eating.
Combine the dressing ingredients in a small bowl or jar. Set aside.
Bring a shallow pot of water to a boil. Add the asparagus and cook 1 minute, or until they turn bright green. Drain and immediately run under cold water to stop the cooking process.
Spread 2 teaspoons of dressing on the bottom half of each roll. Top with ham, cheese, onion, roasted red pepper, asparagus, and arugula. Cover with the top half of the roll.