Heat a grill to medium-high. Clean and lightly oil hot grill. Brush zucchini, onion, and chicken with extra-virgin olive oil. Season with salt and pepper. Grill until zucchini and onion are crisp-tender and chicken is cooked through, 2 to 3 minutes per side. In a small bowl, combine Dijon mustard and mayonnaise.
Spread 1 1/2 teaspoons mustard mixture on top half of rolls. Serve chicken on rolls with grilled vegetables, tomatoes, and baby arugula.
Indoor method: In an oiled grill pan or cast-iron skillet, cook vegetables over medium-high. Wipe skillet clean; cook chicken in same pan.