Preheat oven to 425 degrees F. Lightly oil a large shallow roasting pan or rimmed cookie sheet.

Place poblanos, red bell peppers, sweet potato, and onion onto cookie sheet. Drizzle oil and sprinkle the cumin and minced garlic over top. Add a generous pinch or two of salt and black pepper, then use your hands to mix everything together. After everything is coated well, spread the vegetables evenly in the pan. Roast for 30-40 minutes. Stir the vegetables every 10 minutes while cooking. Remove the pan from the oven and reduce the heat to 350 degrees F.

Prepare a 9x13 pan with nonstick spray. In a small bowl, mix the cilantro in with the salsa. Spread 1/4 cup of the salsa into the bottom of the pan. Add a layer of tortilla pieces to completely cover the salsa. Top with 1/3 of the vegetables, a handful of spinach, and 1/3 of the cheese. Make a second layer of tortilla, salsa, vegetables, spinach, and cheese. Top with another layer. Cover with aluminum foil.

Bake for 20 minutes. Remove the foil and bake another 10 minutes, until cheese is melted and everything is heated through.