Preheat the oven to 400ºF with the one rack set on the upper position, and another set on the lower position.
Combine the almond milk and vinegar in a bowl or measuring cup. Stir, and let sit a few minutes. It’ll curdle—don’t worry. Just stir it again before adding to the flour mixture.
Meanwhile, add the oats to the bowl of a food processor. Pulse until ground into a fine flour—some larger flakes are okay (they add texture to the bread).
Combine all the flours, baking soda and salt to a deep bowl. Whisk together to mix well.
Pour in the almond milk and honey. Stir using a wooden spoon until just combined. The dough will be quite tacky and sticky.
Generously flour a clean countertop or large cutting board. Scrape the dough out onto the surface. Knead briefly, 30 to 60 seconds, until it forms a somewhat smooth ball (it’ll still be a little tacky). Divide into two even pieces. Shape them into balls, and place on a generously floured, rimmed baking sheet. Pat each ball of dough down slightly to flatten into a circle.
Sprinkle the top with a generous amount of flour, 2 to 3 tablespoons. Using a very sharp knife, slash a deep "X" on the top of each loaf, making sure not to cut all the way through.
Bake on the lower rack for 15 minutes. Move tray to the upper rack of oven, and bake for 10 to 12 minutes more, until it becomes a deep golden color and temperature registers 185ºF. It should sound hollow when tapped with your knuckle. Transfer to a wire rack, and let cool completely