If you plan to serve a larger crowd, and have two heavy skillets, two batches of this recipe can be baked at once.
Preheat oven to 425 degrees with rack in center. Place shortening in a 9-to-10-inch cast-iron or other ovenproof skillet, and transfer to oven to heat.
In a medium bowl, whisk together flour, cornmeal, sugar, baking powder, and salt; set aside. In another bowl, whisk together milk and eggs. Pour milk mixture into flour mixture; stir just until combined. Do not overmix; batter should be lumpy.
Carefully slide out oven rack. Pour batter into hot skillet. Cook until cornbread is golden brown and firm to the touch, about 25 minutes. Let stand, uncovered, overnight.