Heat oil in 12-inch skillet over medium-high heat until hot. Add carrots, mushrooms, onion and garlic; cook and stir 1 minute. Add broccoli, corn, chiles, water, oregano, salt and pepper; cover and simmer 4 to 6 minutes or until vegetables are crisp-tender, stirring occasionally.
Add tomato; cook, uncovered, 1 to 2 minutes or until water evaporates and mixture is thoroughly heated.
Spoon 1/4 of vegetable mixture down center of each warm tortilla. Top each with 2 tablespoons cheese. Roll up each tortilla. Serve with salsa and sour cream.