Preheat oven to 375°F (190°C).
Heat olive oil in a medium skillet over medium heat. Add diced onion and cook until softened, about 3-4 minutes.
Add minced garlic and cook for 1 minute until fragrant.
Stir in shredded cooked chicken and taco seasoning mix. Cook for 2-3 minutes, stirring to combine and heat through.
Remove skillet from heat and stir in salsa, black beans, corn, and half of the chopped cilantro.
In a medium bowl, mix sour cream with half of the shredded cheddar and half of the Monterey Jack cheese.
Spread a thin layer of the chicken mixture on the bottom of a 9×13 inch baking dish.
Place two tortillas over the chicken mixture to cover the bottom layer.
Spread half of the sour cream and cheese mixture over the tortillas.
Repeat layering with the remaining chicken mixture, two more tortillas, and the remaining sour cream and cheese mixture.
Top the casserole with the remaining two tortillas and sprinkle the remaining cheddar and Monterey Jack cheese on top.
Cover the casserole with aluminum foil and refrigerate if making ahead, up to 24 hours.
When ready to bake, remove the casserole from the refrigerator and bake covered for 25 minutes.
Remove the foil and bake for an additional 10 minutes or until the cheese is melted and bubbly.
Garnish with the remaining chopped cilantro before serving.