Preheat oven to 350F. Bring all cold ingredients to room temperature.
Combine all dry ingredients in a bowl.
In a separate mixing bowl, beat butter and erythritol until almost white. Add eggs 1 at a time and continue mixing.
Add dry ingredients to wet and mix slowly until combined. Add stevia. Add minced ginger here if you are using wet ginger. Finally, mix in the 1/2 tsp. of apple cider vinegar.
Measure out dough into 6 cupcake holes and bake for 16-18 minutes or until a toothpick comes out clean.
For the icing, powder erythritol in a spice grinder.
Begin beating butter until light and creamy.
Add coconut milk and half of the powdered erythritol. Beat until well mixed. Add the rest of the erythritol and continue mixing until combined.
Use a piping bag to pipe icing onto the cakes once they've cooled.