Preheat gas grill to medium-high or prepare a hot charcoal fire. Set fine-meshed grill rack on top to heat.
Lightly oil grill topper. Grill vegetables in batches until nicely browned and tender, turning often, 5 to 10 minutes. Transfer vegetables to shallow bowl when done. When all vegetables are grilled, cut into thin strips.
Place each tortilla on grill until warm or hot according to package directions. Transfer tortillas to serving plates. Spoon about 1 cup of vegetables onto tortillas. Top each serving with shredded vegan cheese, salsa and cilantro; roll up.