To make the royal icing, beat together erythritol, egg white, 1/2 tsp water, and 1/4 tsp cream of tartar in the work bowl of an electric mixer.
If the icing is too thick, add more water 1/2 tsp at a time, blending after each addition until it is pipeable but still quite thick.
It should be quite stiff. If you add too much water, you can add more erythritol a teaspoon at a time, but try to stay as close as possible to the original recipe so it will dry and hold together.