Heat olive oil in a large oven-safe skillet over medium heat.
Add the chopped onion and cook for 3-4 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Stir in the shredded chicken, ground cumin, chili powder, smoked paprika, salt, and black pepper. Cook for 2-3 minutes until heated through and spices are well combined.
In a medium bowl, whisk together the green enchilada sauce and sour cream until smooth.
Pour half of the enchilada sauce mixture into the skillet with the chicken and stir to combine.
Warm the tortillas in the microwave for 20 seconds to make them pliable.
Spoon about 1/4 cup of the chicken mixture onto each tortilla, roll it up tightly, and place seam side down in the skillet, arranging them side by side.
Pour the remaining enchilada sauce mixture evenly over the rolled tortillas.
Sprinkle the shredded Monterey Jack and cheddar cheeses evenly over the top.
Place the skillet in a preheated oven at 375°F (190°C) and bake for 15 minutes until the cheese is melted and bubbly.
Remove from the oven and let cool for 5 minutes.
Garnish with chopped fresh cilantro before serving.