Make the gravy: Discard all but ½ cup of the cooking oil and return the skillet to the stove over medium heat. (If using a deep fryer, just reserve ½ cup of the oil and add it to a skillet.) Add the remaining ½ cup of flour and cook, stirring constantly, until the mixture is medium brown and looks like milk chocolate. You can easily burn the flour; lower the heat if it begins to smoke, and be sure to keep stirring. Gradually whisk in the 3 cups of chicken stock, and continue to whisk until the mixture has thickened into a gravy. Add generous dashes of salt and pepper to taste. To serve, spoon the gravy over the quail, with a big scoop of butter beans on the side. Serves 6.