Pour the pureed strawberries into a small saucepan. Cook over medium-low heat for approximately 30 minutes, until reduced by half.
Remove from heat and allow to cool to room temperature. You can place it in the fridge for a half hour to speed up the cooling (exact time will depend on how cold your fridge is).
Make the Vegan Strawberry Cake
In a mixing bowl, combine the dry ingredients (flour, cornstarch, baking powder, baking soda, and salt). Set aside.
In the stand mixer, cream together the coconut oil and sugar. Beat on high speed until creamy and well combined.
Slowly whisk in the aquafaba on medium speed.
Add the dairy-free yogurt and vanilla, and mix until combined.
Add the dry ingredients and start mixing on low speed.
Add the almond milk and whisk on medium speed until well combined.
Whisk in the strawberry puree, and mix until the batter is smooth. You may add a couple drops of red food coloring at this point, if you want a more red cake (this is purely aesthetic - I used one drop).
Prepare the cake pans by spraying with non-stick cooking spray and lightly sprinkling with flour.
Pour batter evenly into the two cake pans.
Bake for 30 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Set cakes aside to cool before frosting.
Make the Vegan Strawberry Buttercream Frosting
In a blender, grind the freeze dried strawberries into a fine powder.
In a stand mixer, whisk the coconut oil for a minute until creamy.
Add the confectioner's sugar, almond milk, and vanilla. Whisk on high speed until you have a smooth and creamy frosting.
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