In a large skillet, heat the olive oil over medium heat. Add the chopped onion and garlic, sautéing for 3-4 minutes until soft and fragrant.
- Add the shredded chicken to the skillet, then sprinkle with cumin, chili powder, salt, and pepper. Stir to combine and cook for an additional 2-3 minutes until heated through. Remove from the heat and set aside.
- In a bowl, mix together the sour cream, green enchilada sauce, and diced green chilies until smooth.
- Preheat your oven to 375°F (190°C). Lightly grease a 9×13-inch baking dish. Take each tortilla and spoon a generous amount of the chicken mixture down the center. Roll the tortillas tightly and place them seam-side down in the prepared baking dish.
- Pour the creamy enchilada sauce over the rolled tortillas, spreading it evenly. Sprinkle the shredded cheddar and Monterey Jack cheeses on top of the sauce.
- Bake the enchiladas in the preheated oven for 20-25 minutes, or until the cheese is melted and bubbly, and the sauce is hot.
- Remove from the oven, garnish with fresh cilantro, and serve hot.