Prepare to cook. Preheat the oven to 425 degrees F. Grease a 9-by-9-by-2-inch pan.
Mix the dry ingredients. Sift the flour into a large bowl. Add the sugar, baking powder, psyllium husk and salt and stir.
Cut in the shortening. Cut the shortening into the flour mixture the way you would when making pie dough. You should end up with walnut-size pieces in a sandy flour.
Add the wet ingredients. Combine the eggs and milk in a small bowl. Make a well in the center of the flour mixture and pour in the liquid. Stir with a rubber spatula until everything is combined.
Finish the batter. Stir in the cornmeal, whisking fast, until it is just combined. Do not overstir.
Bake the cornbread. Pour the batter into the prepared pan. Bake until the sides of the cornbread are slightly shrinking from the pan and a toothpick comes out clean, 20 to 25 minutes.
All-Purpose Gluten-Free Flour Mix:
Pour all the flours into a large container. (Restaurant supply stores sell large plastic containers that fit this purpose well. You could also use a large glass jar.) Shake and shake and shake harder until all the flours have become one color.