Preheat oven to 425°F.
In a measuring cup whisk together the oat milk and apple cider vinegar. Set aside. You are making "buttermilk" with this step.
In a small bowl, mix together the water and ground flax. Let this sit while you prepare the remaining ingredients. Soaking the flax allows it to gel which will work to stabilize your batter much like an egg.
In a large bowl, whisk together the flour, sugar, cornmeal, baking powder, baking soda. Pour in the oat milk and vinegar mix. Fold a couple of times. Add in the soaked flax. Fold a couple of times. Let sit while you go on to the next step.
Heat your cast iron skillet over medium high heat until a small pad of butter will quickly melt. This usually takes about 5 minutes of heating. Add in the butter and tilt the pan to move the butter around so that it melts and coats the bottom and sides. Add in the liquid smoke and salt. Stir using a spatula or spoon. Once the butter has completely melted let the pan sit over medium high heat for 1 minute. Remove immediately after 1 minute and pour the melted butter into the batter and use a spatula to scrape out the rest leaving behind just a thin layer of melted butter.
Fold the melted butter into the batter until it is fully incorporated. About 10-12 folds. Pour the batter into the still hot skillet and make sure it is spread out evenly. Place skillet on middle rack of oven. TURN DOWN the heat to 375°F. Bake for 22-25 minutes. Use a toothpick or cake tester to check doneness at the 22 minute mark. Should be cooked all the way through and have a golden top.
Let cool in pan for 10 minutes before slicing and serving. Let cool completely if storing leftovers. Wrap cornbread in foil or in a Ziploc and store on the counter or freeze. Refrigerating bread will dry it out too much.