Put all dry ingredients into your food processor and blend for some seconds. Transfer the dry ingredients into a big bowl.
Whisk the wet ingredients together in a bowl and pour them over the dry ingredients. Use a hand mixer or a whisk to mix everything together.
Grease an 8-inch springform with some oil or line it with parchment paper. Pour the batter into the springform and bake it in the oven at 356 degrees F (180 degrees C) for about 40 minutes (check the center of the cake with a toothpick after 35 minutes to see if it's already done).
Let the cake cool for at least 30 minutes. Then carefully cut cake layers with a big knife. Note: If you have three 8-inch pans, then pour 1/3 of batter into each pan. This way you won't need to cut cake layers for the frosting. The baking time will be less if you use three pans (about 25-30 minutes).
While the cake is in the oven make the buttercream: Process the Erythritol (you can use Xylitol or white sugar instead) in a blender or electric coffee grinder until it's a fine powder. Add milk and starch into a saucepan and bring to a boil. Stir constantly and let simmer for some seconds (it will get thick). Let cool.
Meanwhile, use a hand mixer to whip up the margarine (vegan butter) in a big bowl. Slowly add the powdered sugar, 1 tbsp at a time until nothing is left. You can increase the speed of the hand mixer after a while. Add the peanut butter and once the milk/starch mixture has cooled, add it also slowly to the buttercream while you keep whipping the buttercream for a few minutes.
Spread the frosting onto the cooled cake layers and assemble the cake. Put more frosting on top and on the sides of the cake. Decorate it as per your liking. Put the cake in the fridge before you cut it. Enjoy!