Preheat the oven to 425 F. Position the rack in the center of the oven.
Brush about 1 tablespoon of melted shortening in a 9- to 10-inch cast-iron skillet and put the skillet in the oven.
In a large bowl, combine the cornmeal, flour, baking powder, baking soda, and salt. Whisk to blend thoroughly.
In another bowl, whisk together the buttermilk, egg, and the remaining 3 tablespoons of melted shortening.
Add the buttermilk mixture to the dry mixture and stir just until blended. Carefully remove the hot cast iron pan from the oven and set it on a metal rack. Pour the batter into the sizzling shortening in the hot skillet.
Return the skillet to the oven, reduce the oven temperature to 375 F, and bake for 20 to 24 minutes, until golden brown.
Cut the cornbread into wedges and serve hot with a pat of butter, if desired.