Add the olive oil to a pan and cook the onion until it's lightly browned, about 4 - 5 minutes.
Add the garlic and cook for 1 to 2 minutes or until fragrant.
Add the spices and cook for approximately 1 minute.
Remove from the heat and let cool for 5 minutes.
To the bowl of a blender, add the tomatoes, 1 ½ cups of the broth and all of the pan ingredients.
Blend until smooth, scraping down the sides as needed.
Pour the sauce back into the pan and bring to a simmer over medium heat.
In a small bowl, whisk together the flour and remaining ½ cup of broth until smooth. Pour this into the enchilada sauce, whisking constantly.
Bring the sauce back to a simmer and continue whisking until it begins to thicken.
Turn the heat down to medium-low and cook for 15 minutes to allow the flavors to blend.
When the sauce is done, add 1 cup to the shredded chicken along with the green chilies. Stir to combine and add 1 cup of the cheese. Stir again and set aside.