Grease a 9" round pan or 8" square pan or line a muffin tin, and preheat your oven to 400°F.
Mill the chickpeas, first at a coarse setting and then at a fine setting. Mix the chickpea flour and 3 Tbsp milk substitute in a small bowl and let sit about five minutes.
Do the same double-milling, coarse and then fine, of the dried corn.
In a large bowl, whisk together the flours, sugar, baking powder, and salt.
Gently stir the oil, non-dairy milk, and egg substitute into the dry ingredients until incorporated.
Pour the batter into your prepared pan and bake for 25 minutes or until a toothpick poked in the center of the cornbread comes out clean and the edges of the cornbread turn a golden brown.
Transfer the cornbread to a cutting board or platter and serve warm. Leftovers can be covered and reheated in the microwave for 15 seconds.
