Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper or a silicone baking mat, set aside.
Pour the cake batter, eggs, oil, and 2 teaspoons vanilla extract into a mixing bowl and mix until a batter forms. Drop the dough in tablespoon-sized balls about 2-inches apart onto the prepared baking sheet.
Bake cookies for 8-10 minutes or until golden brown around the bottom edge.
Once cookies are done, remove the baking sheet from the oven and transfer the cookies to a wire rack to cool to room temperature.
For the frosting, add the butter, erythritol, heavy whipping cream, and 1 teaspoon vanilla extract into a mixing bowl. Mix together with a hand mixer for 1-2 minutes or until smooth and creamy.
Add prepared frosting into a piping bag (see note) and pipe frosting onto cooled cookies.
Notes
You can slightly press down on the unbaked cookie dough balls with the bottom of a clean drinking glass to flatten the dough balls and give them more of a cookie shape.
If you don't have a piping bag with a tip, you can use a food storage bag with one corner cut off or just spread the frosting on with a spoon or offset spatula.
The carbs listed for each cookie is 13 grams. After subtracting the sugar alcohols and dietary fibers, each cookie has a net carb amount of 3 grams.