In a large oven-safe skillet, heat olive oil over medium heat. Add the onions and cook until translucent, about 10 minutes. Add the garlic, chicken, and black beans and heat through, about 3 minutes. Remove to a bowl and set aside.
Add the salsa de chile fresco and beef stock to the skillet and turn the heat to high. Bring to a boil, scraping up and bits on the bottom. Remove from the heat and pour the tomato broth into a large measuring cup or bowl. Set aside.
Spray the bottom of the skillet with cooking spray and layer 1/2 of the tortillas then 1/2 of the chicken mixture, 1/2 of the cheeses and repeat.
Pour the tomato broth over the chicken and tortilla mixture and bake for 10 minutes.