Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat. Add the chopped onion and sauté for 4-5 minutes until softened.
Add the minced garlic and chopped jalapeño pepper to the skillet and cook for 1 minute until fragrant.
Stir in the ground cumin, chili powder, smoked paprika, and cayenne pepper. Cook for 30 seconds to toast the spices.
Add the shredded chicken, chicken broth, tomato sauce, diced green chilies, and salt to the skillet. Stir to combine and simmer for 8-10 minutes until the sauce thickens slightly.
Lightly grease a 9×13-inch baking dish.
Warm the corn tortillas in a dry skillet or microwave until pliable to prevent cracking.
Spoon about 1/4 cup of the chicken mixture onto each tortilla, sprinkle with a tablespoon of shredded cheddar and Monterey Jack cheese, then roll up tightly.
Place each rolled tortilla seam-side down in the prepared baking dish.
Pour any remaining chicken sauce evenly over the enchiladas.
Sprinkle the remaining shredded cheddar and Monterey Jack cheese evenly over the top.
Bake in the preheated oven for 15-20 minutes, or until the cheese is melted and bubbly.
Remove from oven and let cool for 5 minutes.
Garnish with chopped fresh cilantro and serve with sour cream on the side.