In a medium saucepan, heat the oil and flour on medium heat. Whisk together and bring to a boil. Allow to boil for around 1 minute.
Add in the spices and mix until a thick paste forms. Add in the chicken broth and whisk well. Bring to a boil, then reduce the heat and allow to simmer for 10 minutes, or until thickened.
Preheat the oven to 400°F.
Pour 1/2 a cup of sauce into a 9x13 baking pan.
Spread 2 Tbsp enchilada sauce along the middle of a corn tortilla. Top with around 2 Tbsp shredded chicken then sprinkle with some of each of the cheeses and roll up. Place in the prepared baking sheet and repeat with the remaining tortillas.
Top the rolled enchiladas with the remaining sauce and cheese and bake in the preheated oven for 20 minutes.