Prepare smoker using manufacturer 's instructions using either alder or apple chips. Place veggies in single layers on smoker racks. Smoke for about 30 minutes.
Preheat grill for high heat.
Brush grate with oil. Arrange vegetables on grill, with the peppers away from the center. Cook for 10 to 15 minutes, turning once. Baste with teriyaki sauce frequently. Vegetables will cook at different rates; remove tender pieces from the grill, and continue cooking until all are done.
