Mix the flours and all other dry ingredients (except cornmeal) in the bowl of a food processor or stand mixer. Add the shortening and pulse the food processor or run the mixer to cut in the shortening into the flour, like you would for a pie crust. When the mixture looks like clumpy cornmeal, you're done. (You can also do this by hand, with two knives or a pastry cutter.)
Beat together the eggs and milk in a small bowl. Make a well in the center of the dry ingredients and pour in the liquid. Stir with a spatula until just combined. Stir in the cornmeal until just combined. Do not over mix.
Pour into a greased 9x9 square pan. Bake 20 to 25 minutes, or until the sides of the cornbread are slightly shrinking from the pan and a toothpick comes out clean.
Notes
This recipe is an adaptation of one from the Gluten-Free Girl website.
Substitutions
Don't substitute butter or margarine for the shortening, but lard works very well. You can use Crisco or one of the new trans-fat-free types.
Corn Substitutions: Corn is a common ingredient in products. Starch, modified food starch, dextrin and maltodextrin can be from corn. Consult with your physician to find out which corn derivatives you need to avoid. Many corn-free options are available in the US. Find out more about corn substitutions.
Egg Substitutions: There are many egg-free products and foods available to make your recipes free of eggs. Find out more about egg substitutions.
Gluten: Gluten is a protein found in specific grains (wheat, spelt, kamut, barley, rye). Other grains are naturally gluten-free but may have cross-contact with gluten-containing grains. Look for certified gluten-free products if you need to avoid gluten. Find out more about wheat and gluten substitutions.
Milk and Soy Substitutions: Alternative dairy-free milk beverages and products will work in most recipes. Find out more about milk substitutions and soy substitutions.