Place a large baking sheet in the oven. Preheat the oven to 450° (leave the pan in the oven as it preheats).
Place first 3 ingredients in a saucepan over medium heat; cook 4 minutes, stirring occasionally.
Heat a large skillet over medium-high heat. Add oil; swirl. Add zucchini; sauté 2 minutes. Add oregano, cumin, black pepper, red pepper, and garlic; cook 2 minutes. Remove from heat.
Prepare rice according to package directions.
Warm tortillas according to package directions. Spread about 1/3 cup bean mixture evenly over each tortilla, leaving a 1/2-inch border. Top each tortilla with 1/3 cup rice, 1/3 cup zucchini mixture, and 2 tablespoons cheese. Fold in sides of tortilla over filling; roll up. Repeat procedure with remaining 7 tortillas, bean mixture, rice, zucchini mixture, and cheese.
Lightly coat burritos with cooking spray. Arrange burritos, seam sides down, on preheated baking sheet. Bake at 450° for 4 minutes, turning after 2 minutes. Top each serving with 1 tablespoon sour cream, 1 tablespoon pico de gallo, and cilantro sprigs, if desired, or follow freezing instructions.