Arrange cut vegetables on large rimmed baking pan. Brush both sides with olive oil and squeeze juice of 1/2 lime over vegetables. Combine cumin, chili powder, salt, cayenne and black pepper to taste in small bowl. Sprinkle on veggies.
Heat grill. Arrange vegetables on oiled grate or in grill pan. Grill 8 to 10 minutes, turning as necessary, until warm and tender, adding avocado halves halfway through, cut-side down.
Chop veggies and slice avocados. Season with salt and pepper, if desired. Serve in warm tortillas with wedges of remaining lime. Top with cheese and garnish with cilantro.
TIP: To warm tortillas on grill, arrange tortillas in single layer on hot grate. Heat 2 to 3 minutes until warm through and small brown spots appear, turning once or twice.