Preheat the oven to 375°F (190°C). Lightly grease a 9×13 inch baking dish.
Heat the vegetable 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 chopped jalapeño pepper to the skillet. Cook for 1-2 minutes 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, tomato sauce, chicken broth, tomato paste, and salt to the skillet. Stir well to combine and simmer for 5 minutes until the sauce thickens slightly. Remove from heat.
Warm the corn tortillas in a dry skillet or microwave until pliable to prevent cracking when rolled.
Spoon about 1/4 cup of the chicken mixture onto each tortilla. Sprinkle a tablespoon of cheddar and Monterey Jack cheese over the filling, then roll up the tortilla tightly.
Place the rolled enchiladas seam side down in the prepared baking dish in a single layer.
Pour any remaining sauce from the skillet evenly over the enchiladas.
Sprinkle the remaining shredded cheese evenly over the top of the enchiladas.
Bake in the preheated oven for 20 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let cool for 5 minutes. Garnish with chopped fresh cilantro and serve with lime wedges.