Preheat the oven to 350°F.
Heat the oil in a large skillet over medium heat. Add the peppers to the skillet and cook until softened, 5-6 minutes. Remove the skillet from the heat and stir in the cream of mushroom soup, cream of chicken soup, Ro-Tel tomatoes, chicken broth, sour cream, cumin, chili powder, and oregano. Reserve 1 cup of the sauce.
To assemble the layers, spread 1/2 cup of the sauce into the bottom of a 9 x 13 baking dish. Spread half of the chicken in an even layer over the sauce, then pour half of the remaining sauce over the top. Sprinkle 1 cup of the shredded cheese over the top, then layer half of the tortillas in an even layer over the cheese. Spread the remaining chicken over the top of the tortillas, then pour the remaining sauce over the chicken. Sprinkle with 1 cup of cheese, then spread the remaining tortillas evenly over the top of the cheese. Pour the 1 cup of reserved sauce over the top, then sprinkle with the remaining 1/2 cup of cheese.
Bake for 40 minutes, until heated through and bubbling. Turn the oven to broil, and broil for 2-3 minutes, until golden brown on top.
Let cool for 5-10 minutes before serving.