Preheat the oven to 350°F (175°C). Grease and lightly flour a 9×9-inch baking pan or line it with parchment paper.
Mix the Dry Ingredients: In a large bowl, whisk together the all-purpose flour, sugar, baking soda, and salt until well combined.
Add Wet Ingredients: Make three small wells in the dry mixture. Into one well, add the vinegar. In the second, add the vanilla extract. In the third, pour in the vegetable oil.
Combine with Water: Pour the cold water over the entire mixture. Stir everything together until smooth and well combined. The batter will be thin, which is normal.
Bake: Pour the batter into the prepared pan and bake in the preheated oven for about 30 minutes, or until a toothpick inserted in the center comes out clean.
Cool: Allow the cake to cool in the pan for 10 minutes, then transfer it to a cooling rack to cool completely.
Make the Frosting: In a medium bowl, beat together the powdered sugar, vegan butter (or regular butter), vanilla extract, and almond milk. Stir until smooth and creamy.
Frost the Cake: Once the cake is completely cool, spread the frosting evenly over the top using a spatula or knife.
Serve: Slice the cake into pieces and serve. Enjoy your delicious, moist vanilla crazy cake!