Preheat the oven to 350 F. Prepare a 2 quart baking dish or casserole. I used a smaller, deeper pan, and it took a little longer, so adjust your time, and test with a toothpick.
In a large bowl, combine the flour, cornmeal, baking powder, brown sugar and salt, and stir to mix well. In a cup, mix the almond milk with cider vinegar, flax and oil. Let stand for five minutes.
Spread the peaches in the baking dish. Stir the almond milk mixture well, then pour over the flour mixture and stir to mix until pretty smooth. Pour the cornmeal topping over the peaches in the dish and smooth the top.
Bake for 50 minutes to an hour and 10 minutes, until the peaches are bubbling around the edges of the pan, and the cornbread is golden brown. Test the topping with a toothpick inserted into the center of the pan, testing just the topping. It should be baked through, with no wet batter. Let cool for 5-10 minutes before serving, with a scoop of your favorite ice cream.