Add 1/4 cup of water to the 4 teaspoons of agar-agar powder and mix well, set aside.
Add 1 cup of sugar and the remaining water to a small sauce pan and warm it over a medium-low heat. Gently mix until the sugar has dissolved.
Bring the sugar mix to a boil and then add in the agar mixture, mixing well. Increase the heat to keep the mixture boiling.
While the sugar mixture boils for 2 minutes, add 1/4 cup aquafaba and 1/4 teaspoon cream of tartar to a large mixing bowl. Beat the mixture until it is frothy.
Once the sugar mixture has fully boiled for a few minutes, slowly add it to the aquafaba mixture, while beating at the same time. Beat the mixture until it is fluffy like marshmallow cream.
Add the cream to a piping bag. Pipe a dab of cream on a cookie, place the stick, and then cover the stick line with more cream. Then top off with another cookie.
Do this for all the cookies and then let them sit for about an hour for the cream to firm up.