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To make the crust:.
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In a food processor, pulse the flour, cornmeal, and salt a few times.
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Cut the butter and shortening into small cubes, add to the flour mixture, and pulse until the butter is broken up into pea-sized and smaller chunks.
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Stir together the vinegar and water, and add to the butter-flour mixture a tablespoon at a time, pulsing just until the dough comes together.
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Press into two disks one larger (to line the pan), and the other smaller (for the top).
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Wrap in plastic wrap and refrigerate while you prepare the filling.
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To make the filling:.
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Preheat the oven to 375F.
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Heat a large stockpot over medium-high heat and add 1 tbsp olive oil.
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Stir in the garlic and onion and cook until the onion is translucent.
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Add the chicken, and cook, stirring, until the chicken is no longer pink.
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Transfer to a bowl and set aside.
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Wipe out the pan and return to medium-high heat.
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Add 2 tbsp olive oil and stir in the flour.
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Cook, stirring constantly, until it turns a nice golden-brown.
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Add the vegetables, tomatoes, and chicken broth and stir well.
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Stir in the salt, chile powder, and cumin and partially cover the pot.
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Cook for about 30 minutes, stirring occasionally.
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Meanwhile, roll out the larger dough disk, and press into a 2 1/2 quart casserole dish.
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Line the inside of the dough with foil, shiny side down, and bake for about 10 minutes.
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Remove the foil and set the dish aside.
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Roll the other disk of dough out to fit over the top of the casserole dish, and set aside.
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When the filling has thickened and the chicken has cooked through, transfer to the dough-lined dish.
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Press the sheet of dough on top, and cut a few slits in it so steam can escape.
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Bake for about 30 minutes, or until the crust is nice and golden.