Preheat your oven to 375°F (190°C) and lightly grease a medium baking dish with a little of the olive oil or a quick spritz of cooking spray.
Warm the olive oil in a skillet over medium heat, then add the finely chopped yellow onion and cook for about 3 to 4 minutes, stirring often, until the onion softens and turns slightly translucent.
Stir the cooked shredded chicken into the skillet with the onion and sprinkle in the ground cumin, chili powder, garlic powder, salt, and black pepper, mixing well so the chicken is evenly coated with the seasonings.
Pour in 1/2 cup of the enchilada sauce into the skillet, stir to combine with the chicken mixture, and let it warm through for 1 to 2 minutes, then remove the skillet from the heat.
In a small bowl, combine 1 cup of the shredded cheddar cheese with the shredded mozzarella cheese and set this cheese mixture aside for filling and topping the enchiladas.
Spread 1/2 cup of the remaining enchilada sauce evenly over the bottom of the prepared baking dish to create a thin layer.
Lay one flour tortilla on a clean surface, spoon about 1/4 cup of the warm chicken mixture in a line down the center, and sprinkle a small handful of the cheese mixture over the chicken.
Roll the tortilla snugly around the filling and place it seam-side down in the sauced baking dish; repeat with the remaining tortillas and chicken mixture until the dish is filled.
Pour the rest of the enchilada sauce evenly over the rolled tortillas, making sure the tops are well covered so they do not dry out while baking.
Sprinkle the remaining cheese mixture evenly over the top of the sauced enchiladas, covering as much of the surface as possible.
Place the baking dish in the preheated oven and bake the enchiladas for 18 to 20 minutes, or until the cheese is melted and bubbling and the edges of the tortillas are lightly golden.
Carefully remove the baking dish from the oven and let the enchiladas rest for about 5 minutes so they can set slightly and are easier to serve.
Spoon small dollops of sour cream over the top of the enchiladas and sprinkle with the chopped fresh cilantro just before serving.