In a large mixing bowl, add the vegan butter and brown sugar. Using a hand mixer or stand mixer, beat until fully combined and fluffy.
Now add the applesauce and vanilla. Continue to beat until everything is combined. Set aside.
In a medium sized mixing bowl, sift the flour and baking soda. Stir in the salt.
Add the dry ingredients to the wet a little at a time. Continuing to mix, until everything is combined and the dough comes together. It may seem crumbly as you mix, but it will be perfect once fully combined.
Divide the dough in half, and flatten each piece into a disk. Wrap each in parchment paper and put in the fridge. Chill for at least 1 hour.
When ready to bake, preheat the oven to 350 degrees(F).
Take one disk at a time and place on a generously floured surface. Sprinkle the top with more flour and spread some flour on a rolling pin. Roll out, starting from the center and working your way out to about 1/4 inch thick.
Cut into any shape you want, place each cookie on a baking sheet about an inch apart. Bring all the scraps of dough back together and form another dough ball, flatten out and chill again to make more cookies with.
Bake the cookies for 10-12 minutes or until firm. Repeat with all the dough.
Cool completely, then make the frosting.
In a large mixing bowl, beat together the vegan butter and vegetable shortening. Then add the powdered sugar a little at a time. Beating until all the sugar is incorporated. Add the vanilla and salt. Beat again to combine.
Spread the frosting on the cookies and top with sprinkles if desired.