Heat olive oil in a large skillet over medium heat.
Add the chopped onion and cook for 3-4 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Stir in the shredded chicken, ground cumin, chili powder, smoked paprika, salt, and black pepper. Cook for 2 minutes to combine flavors.
In a medium bowl, mix together the enchilada sauce and sour cream until smooth.
Reduce heat to low. Pour half of the enchilada sauce mixture into the skillet with the chicken and stir to combine.
Remove the skillet from heat. Spoon about 2 tablespoons of the chicken mixture onto each tortilla, roll it up tightly, and place seam side down back into the skillet, arranging them snugly in a single layer.
Pour the remaining enchilada sauce mixture evenly over the rolled tortillas in the skillet.
Sprinkle the shredded Monterey Jack and cheddar cheeses evenly over the top.
Cover the skillet with a lid and cook over low heat for 8-10 minutes until the cheese is melted and the enchiladas are heated through.
Remove from heat and sprinkle chopped fresh cilantro on top before serving.