Preheat oven to 350°
In a large mixing bowl, beat the softened vegan butter and sugar on a high speed until it appears whipped (about 1½ minutes). I used a standing mixer, but you can also use a hand mixer as well.
Add in the vanilla extract, flour, salt, baking soda, applesauce and water. Continue mixing until a dough is formed.
Take the ball of dough and place it between two large sheets of parchment paper to avoid sticking. Push down on the dough with your hands to flatten, then roll the dough out with a rolling pin until it's about ¼- ¾ inches thick.
Use cookie cutters to cut out each cookie and transfer to a baking sheet.
Once all of the cookies have been cut, form the dough back into a ball, flatten, then roll out between the sheets of parchment paper again. Cut out the cookies and transfer to the baking sheet. Repeat process until finished.
Bake for 8-10 minutes.
Remove from oven and let cool completely before icing.
Mix together the ingredients for the icing (if using multiple food colorings, separate plane icing into different bowls, then add food coloring of choice to each).
Once the cookies have cooled and they are ready to ice, use a squeeze bottle or icing bag and tip to design your cookies as you wish.