Preheat oven to 160°C (325°F). Grease a 9-inch round springform pan with coconut oil or butter. Cut out a piece of parchment paper into a 9-inch circle and stick it to the bottom of the pan. Grease the paper and pan sides again.
In a large mixing bowl, whisk eggs with sugar-free sweetener, oil, and vanilla. Process as if you whisked a breakfast omelet.
Whisk in almond flour and baking powder until evenly combined.
Pour the vanilla cake batter into the prepared pan.
Bake for 25 minutes in the center of your oven. The cake is cooked when a skewer inserted in the middle comes out clean.
Cool for 5 minutes in the pan, then release the cake on a cooling rack. Cool for 1 or 2 hours before adding the frosting.
Repeat the vanilla cake recipe to create a second vanilla cake.
Add the soft butter cubes and vanilla to a stand mixer. Mix on high speed until it forms a pale, smooth, and fluffy butter.
Gradually add the sugar-free powdered sweetener, mixing on medium speed for 2 minutes until it forms a fluffy cream.
Add cream and keep whisking for 1 minute to incorporate.
Spread the frosting between the 2 cake layers and on sides using an icing spatula.
Place the cake in the fridge for 2 hours to set up the frosting if desired.
