Preheat your oven to 350F. Lightly grease a 9 x 13 rectangular baking dish and line the
bottom with a piece of rectangular parchment paper.
Whisk the flours, baking powder and soda, and salt together in mixing bowl (or the bowl of a stand mixer).
In the bowl of a stand mixer or in a large mixing bowl with an electric mixer, mix the oil,
water, sugar, and vanilla extract together until well-mixed. Add the non-dairy milk and lemon juice and mix well. Add dry ingredients in two additions, mixing on medium speed as you go. When the batter is well mixed (just when no lumps are visible), pour ¾ of the batter into your prepared baking dish. Cover this layer with the halved, frozen cherries. Use a spoon to drop the rest of the batter on top of the cherries. They should be mostly covered, with some still peeking out from under the batter.
Transfer the baking dish to your oven. Bake for 45 minutes, or until the edges are golden brown and the top is set. Cool the cake completely. If you’d like to glaze it, whisk together 1 cup of powdered sugar and two tablespoons of non-dairy milk till smooth, then pipe or drizzle it over the top of the cake. Cut into slices and enjoy!