Heat oven to 425°F. Place chopped zucchini, squash, red and green bell pepper and onion on a baking sheet; toss with taco seasoning and 2 teaspoons olive oil. Roast vegetables in oven, stirring once, until crisp and golden, about 20 minutes.
Meanwhile, heat a large skillet over medium heat on the stovetop. Add remaining 2 teaspoons of olive oil, then add spinach and mushrooms. Cook, stirring occasionally, until all the liquid from the mushrooms is absorbed, about 5 to 7 minutes. Remove from heat; drain.
Decrease oven temperature to 375°F. In a large bowl, stir together roasted vegetables, mushroom and spinach mixture and green chiles. Scoop two heaping spoonfuls of vegetable mixture on top of each tortilla; sprinkle with shredded cheese. Fold in sides, then roll up completely. Place seam-side down in a lightly greased 13-by-9-inch baking pan. Repeat with remaining tortillas (you may not use all the filling).
Lightly spray tops of burritos with cooking spray. Bake until golden brown, about 15-20 minutes. Remove from oven; serve immediately with salsa and sour cream.
Disclosure: I received compensation from Old El Paso for recipe development purposes. All opinions are my own.