Melt the butter in a medium saucepan over medium heat. Whisk in the flour, and cook until toasty, about 3 minutes. Add the garlic and cook for 1 minute more. Gradually whisk in the chicken stock, stirring well to avoid any lumps. Stir in the milk, salt, green chile, and oregano, and cook over medium heat until thickened and bubbly, about 15 minutes, stirring often.

Place the chicken in a medium sauce pan with a lid. In a small bowl, combine the chicken stock and flour, whisking well to combine. Pour the stock and flour mixture over the chicken, and stir to combine. Add the salt, red chile powder, 2 tablespoons chopped green chile, and minced onion, and stir to combine. Cover and cook over medium heat for 20 minutes until bubbly, stirring often.

In a greased 9x13 pan, ladle in 1/4 of the prepared green chile sauce. Layer 16 of the tortilla quarters on top of the sauce so that they form a layer that covers the bottom of the pan. Top with half of the prepared chicken mixture and sprinkle with 1/2 cup of the cheese. Cover with 1/2 cup of sauce. Top with an additional 16 tortilla quarters, and then layer on the remaining chicken mixture, 1/2 cup of cheese and an additional 1/2 cup of sauce. Top with the remaining tortilla quarters, and then cover with the remaining sauce and sprinkle with the remaining cheese.

Bake at 350 for 25-30 minutes, until thickened and bubbly. Allow to rest for 10 minutes before serving. If desired, garnish with lettuce and tomatoes.