A skillet of cornbread is the traditional accompaniment for black-eyed peas in the Southwest.
Heat oven to 425 degrees with rack in center. Place shortening in an 8-inch cast-iron skillet. Place in oven.
In a medium bowl, whisk together the flour, cornmeal, sugar, salt, and baking powder. Set aside. In a small bowl, whisk together the milk and eggs until frothy. Pour the milk-egg mixture into the dry ingredients. Mix just until ingredients are incorporated. Do not overmix; batter should be lumpy. Carefully remove hot skillet from oven. Pour batter into it; return to oven. Cook until top is golden brown and a skewer inserted in the center comes out dry, 25 to 30 minutes. Serve warm.