Preheat the oven to 375°F (190°C).
In a medium saucepan, heat the vegetable oil over medium heat.
Add the chopped onion and cook until softened, about 3-4 minutes.
Add the minced garlic and cook for another 30 seconds until fragrant.
Stir in the all-purpose flour and cook for 1 minute, stirring constantly.
Add the chili powder, ground cumin, dried oregano, cayenne pepper, and salt; stir to combine.
Slowly whisk in the chicken broth and tomato sauce, ensuring no lumps form.
Bring the sauce to a simmer and cook for 8-10 minutes until slightly thickened.
Remove the sauce from heat and stir in the diced green chilies.
Warm the corn tortillas in a dry skillet or microwave until pliable.
Dip each tortilla into the enchilada sauce to coat both sides.
Place about 1/4 cup of shredded chicken and a tablespoon of shredded cheddar cheese on each tortilla.
Roll up the tortilla tightly and place seam-side down in a 9×13 inch baking dish.
Repeat with remaining tortillas and filling.
Pour the remaining enchilada sauce evenly over the rolled tortillas.
Sprinkle the shredded cheddar and Monterey Jack cheeses evenly on top.
Bake in the preheated oven for 20 minutes, or until the cheese is melted and bubbly.
Remove from oven and let cool for 5 minutes.
Garnish with chopped fresh cilantro.
Serve with sour cream and sliced avocado on the side.