1. Prepare a charcoal or gas grill for high heat (450° to 550°; you can hold your hand 5 in. above cooking grate only 2 to 4 seconds). Meanwhile, heat 1 tbsp. oil in a large frying pan over medium-high heat. Cook onion, chiles, and nopales until softened and starting to brown, about 5 minutes. Season with salt and remove from heat.
2. Lay 4 tortillas on a baking sheet. Sprinkle each with 1/4 cup cheese and 1/2 cup warm vegetable mixture. Top each with a second tortilla.
3. Using a wad of oiled paper towels and tongs, oil cooking grate. Use a spatula to transfer quesadillas to grill; cook, turning once, until grill marks appear and cheese is melted, about 2 minutes. Remove from grill, cut each into quarters.
4. In a small bowl, combine cabbage, salsa, lime juice, cilantro, and a pinch of salt. Serve quesadillas with slaw, and sour cream if you like.
Note: Nutritional analysis is per serving.