In a heavy frying pan over medium high heat, cook flour, stirring constantly, until flour is a light toast color. Set aside to cool. In a Dutch oven or large skillet, add the butter and sauté the onion for 10 minutes, or until soft and translucent. Add garlic and cook for 3 minutes. Remove to a plate and set aside. In the same skillet, over high heat, add 2 tablespoons of olive oil and brown the pork until seared on the outside and cooked. Add the onion and garlic mixture and salt, stirring to combine. Stir in the browned flour, mixing thoroughly. Add chicken broth and over medium heat, cook until thickened. Add tomato sauce, tomatoes green chile and oregano. Cover and simmer for 50 minutes. Meanwhile, make the dumplings. In a medium bowl, combine flour, cheddar cheese, cornmeal, and baking powder. In a small bowl, mix beaten egg, milk, and oil. Add to flour mixture, and stir with a fork until just combined. Drop dumplings by tablespoonfuls into chili. Cover and cook for 15 minutes or until dumplings are cooked through.