Before starting, make sure all of your ingredients for this vegan white cake are at room temperature, otherwise your cake will bake up weird. Warm the soy milk and aquafaba in the microwave for a few seconds if you need to
Preheat the oven to 350°F (make sure you are not using convection mode, this will cause the cake to bake unevenly). Line two 9-inch cake pans with circles of parchment paper on the bottom. Do not flour or grease the pans.
In a small bowl, whisk together the aquafaba and cream of tartar vigorously until the aquafaba is fluffy and foamy, and set aside. No need to whip it to stiff peaks, just get it foamy.
In another small bowl, stir together the soy milk, 2 tsp vinegar, vanilla and butter flavors, and set aside. The soy milk will curdle a little bit; this is normal.
Sift all of the dry ingredients (including the sugar) into a mixing bowl and stir well, sifting a second time if the mixture still appears lumpy. Don't skip this step - sifting is important!
Add the vegetable oil and shortening into the bowl. Use a strong fork to break up the shortening and then mix everything together well. The mixture will first turn crumbly like a shortbread dough and then as you continue to mix, will start to resemble wet sand. This will take some elbow grease. Make sure to scrape around the bottom of your mixing bowl to get any flour pockets hiding out there. Continue until the mixture is fully smooth.
Add 1/3 of the wet ingredients to the bowl and mix until combined. Add another 2/3 and repeat. Finally, add the remaining 1/3 and mix until the batter is very smooth and runny, which will take a minute or two.
Give the aquafaba mixture another whisk to get it foamy again, as it may have deflated a bit while you were mixing the rest of the cake. If it's still partially liquidy, take only the foamy part and not the part that is liquid. Then, whisk it into the cake batter until mixed in evenly (if you only fold it in, you might get streaks or a gummy layer - mix well if needed). Divide the cake batter between your two cake pans.
Bake the vegan white cake layers for approximately 24-28 minutes, or until a toothpick inserted into the center comes out clean and dry. Be sure not to open the oven until it has been at least 15 minutes (preferably longer), otherwise you will risk your cakes deflating when you open the oven door.
Let the cakes cool in their pans on top of a cooling rack for about 10 minutes. You can then run a sharp knife around the edges of the pans before very gently inverting the cakes to cool completely. I recommend lightly flouring or spraying your cooling rack before flipping the cakes onto it; they are very moist and have a tendency to stick. After flipping them over, gently peel off the parchment paper.
These cakes can be layered and frosted once completely cooled (and the layers can be gently evened out if needed, although they tend to bake pretty flat). Top with vanilla buttercream frosting and serve with raspberry sauce. Leftover cake can be stored covered in the fridge for a couple of days. If your layer cake is fully frosted it can also be stored covered at room temperature. If stored in the fridge, it's recommended to bring it to room temperature before slicing, to reduce crumbliness.