The enchilada fillingincludes summer squash,mushrooms, eggs, and cheese.
Wrap tortillas in a clean kitchen towel; place in a bamboo steamer basket. Fill a wok with 2 inches water; bring to a boil. Reduce heat to medium; set steamer in wok. Steam tortillas until softened, 6 minutes. (Or wrap tortillas in a damp, clean kitchen towel, and heat until softened, 10 to 15 seconds in a microwave or 7 to 10 minutes in a 200 degrees oven.) Set aside.
Preheat oven to 375 degrees. Heat oil in a large nonstick skillet over medium-high heat until hot but not smoking. Cook corn, stirring, until just caramelized, about 5 minutes. Add shallot, zucchini, summer squash, and mushrooms; cook, stirring, until tender, about 4 minutes. Season with salt and pepper. Transfer to a bowl.
Vigorously whisk eggs and cream until blended. Season with salt and pepper. Heat butter in a large nonstick skillet over medium-high heat until foamy. Add egg mixture; cook, stirring, until scrambled but not dry, about 4 minutes.
Pour 1/2 cup red chile sauce along one long side of a 9-by-13-inch baking dish; pour 1/2 cup green chile sauce along opposite long side (sauces should meet).
Spread 1 tablespoon red chile sauce on 1 tortilla; sprinkle 2 tablespoons cotija over entire surface. On bottom third of tortilla, place 4 1/2 teaspoons each egg and corn mixture, 1 teaspoon tomatoes, and 1/2 teaspoon cilantro. Firmly roll tortilla; place in baking dish, seam side down. Repeat with remaining tortillas.
Pour 1/2 cup each red and green chile sauce on top of enchiladas, mirroring the sauces on the bottom. Sprinkle with queso blanco. Bake until heated through, about 25 minutes. Garnish with remaining 2 tablespoons cilantro, and serve with remaining chile sauce.
You can use shredded Monterey Jack cheese in place of the cotija and queso blanco. Other wild mushrooms, such as shiitakes, can be substituted for porcini.