Heat oven to 350ºF.
Combine the chiles, garlic, chili powder, cumin, chicken broth, tomato sauce, salt, and pepper in a medium saucepan and put over high heat.
Bring to a boil then reduce the heat to low and simmer for 15 minutes or until the chiles are soft. Set aside until ready to use.
Heat the vegetable oil in a large skillet over medium-high heat. Saute the chicken until just cooked through, approximately 7 to 9 minutes. Move the chicken from the pan to a plate or bowl. Add the onions to the same pan along with a generous pinch of salt, decrease the heat to medium-low and sweat for 4 to 6 minutes. Add the garlic and oregano and cook until the onions are tender, 2 to 3 minutes more. Add the chicken back to the pan, stir to combine and remove from the heat.
Halve 3 of the tortillas
Lube a 9-by-13-inch glass baking dish with nonstick spray then dose half a cup of the sauce into the bottom of the dish. I usually spread it around with a large rubber spatula.
Dip 4 tortillas (three whole and one cut into halves) into the remaining sauce and lay them into the bottom of the dish. Cut 1 of the tortillas in half to evenly cover the bottom of the dish.
Top this with half of the chicken mixture and 1 cup of the cheese. Repeat layering finishing with the remaining sauce and remaining cup of cheese.
Cover with foil and bake in the middle of the oven for 30 minutes. Then remove the foil and bake an additional 10 minutes, or until cheese on top is bubbly.