Preheat oven to 450°F. Grease two 6 or 7-cavity corn stick pans with about 1 tablespoon of shortening or oil per pan, coating every curve of each cavity. Place the greased pans in the hot oven to preheat for about 5 minutes.
In a large bowl, whisk together cornmeal, flour, sugar, salt, baking powder, and baking soda. Add buttermilk, egg, and vegetable oil (or melted shortening). Stir just until the batter comes together. Do not overmix.
Carefully remove the hot corn stick pans from the oven. Fill each cavity with batter, almost to the top (leave about ⅛ inch).
Bake until light golden brown on top, about 14-16 minutes for larger corn sticks (in 6-cavity pans) or 12-14 minutes for smaller corn sticks (in 7-cavity pans). The bottoms will be darker and crispier.
Remove corn sticks from pans immediately and serve warm.
If you have extra batter, re-grease one of the hot pans and bake another batch.