Step 1: Prepare the Creamy Chicken Filling
Preheat your oven to 375°F (190°C). Lightly grease a 9×13 inch (23x33cm) baking dish. In a large bowl, combine the softened cream cheese, sour cream, cumin, oregano, and garlic powder. Beat with a hand mixer or stir vigorously until smooth. Stir in 1 cup of the salsa verde, the lime juice, and chopped cilantro. Gently fold in the shredded chicken until it is evenly and thoroughly coated in the creamy, tangy mixture.

Step 2: Warm the Tortillas (Crucial Step!)
To prevent the corn tortillas from cracking, briefly warm them. You can: a) Wrap a stack of 5-6 in a damp paper towel and microwave for 45-60 seconds, or b) Quickly dip each tortilla in the remaining salsa verde to lightly coat and soften it. This makes them pliable and helps them absorb flavor.

Step 3: Assemble the First Layer
Spread about ½ cup of the remaining plain salsa verde over the bottom of the baking dish. Arrange a layer of warmed tortillas over the sauce, overlapping slightly and tearing some to fit, to create a complete base layer.

Step 4: Build the First Flavor Stratum
Spread half of the creamy chicken mixture evenly over the tortillas. Sprinkle with half of the diced onion, half of the drained black beans (if using), half of the corn, and half of the diced green chiles. Sprinkle with 1 cup of the Monterey Jack cheese and ½ cup of the cheddar cheese.

Step 5: Repeat the Layers
Add another layer of warmed tortillas. Spread the remaining creamy chicken mixture over them. Top with the remaining diced onion, black beans, corn, and green chiles. Sprinkle with another 1 cup of Monterey Jack and ½ cup of cheddar cheese.

Step 6: Add the Final Tortilla Layer and Sauce
Place a final layer of tortillas on top. Pour the remaining salsa verde evenly over the entire surface, using a spoon or spatula to spread it so all tortillas are coated. This is essential for moist, flavorful tortillas.

Step 7: Apply the Cheese Blanket
In a bowl, combine the remaining 1 cup of Monterey Jack and 1 cup of cheddar cheese. Sprinkle this blend evenly over the saucy top. Then, evenly sprinkle the crumbled Cotija cheese over everything.

Step 8: Bake to Bubbling, Golden Perfection
Cover the dish tightly with aluminum foil. Bake for 25 minutes. Then, remove the foil and bake for an additional 15-20 minutes, or until the cheese is completely melted, the edges are bubbling, and the top is lightly golden.

Step 9: Prepare the Crema Drizzle and Finish
While the casserole bakes, whisk together the Mexican crema (or sour cream) with the 2 tablespoons of milk to create a drizzle-able consistency. Once the bake is out of the oven, let it rest for 10-15 minutes—this allows the layers to set for clean cutting. Drizzle the crema mixture artistically over the top. Garnish lavishly with sliced green onions, diced avocado, pickled red onions (if using), fresh cilantro, and radish slices. Serve immediately with lime wedges on the side for squeezing over each portion.