Arrange racks in top and bottom third of oven. Preheat broiler to high.
Meanwhile, thinly slice peppers and onion. Cut chicken into bite-size pieces. Place veggies and chicken on Sheet Pan. Add oil and seasoning; toss to evenly mix, then spread out in a single layer.
Broil, rotating pan and stirring often, until cooked through, 8–10 min.
Wrap tortillas in foil; place on bottom rack in oven for last 3 min of cooking.
Remove both from oven; sprinkle cheese over chicken mixture. Serve in warm tortillas with toppings, as desired.