Make the cookies, in a stand mixer bowl or large mixing bowl add the vegan butter and sugar.
Beat with the paddle attachment in the stand mixer or using a hand mixer, until the butter and sugar are fully combined and light and fluffy.
Then add the applesauce and vanilla, continue to mix until fully combined, scraping down the sides as needed. Set aside.
Now, sift the flour and baking soda into a large mixing bowl, stir in the salt. Add the dry ingredients a little at a time to the wet ingredients. Continuing to mixing until fully combined and the dough forms a ball. It may seem dry at first, just keep mixing until it comes together.
Put the dough into parchment paper or plastic wrap and chill in the fridge for 30 minutes.
When ready to bake, preheat the oven to 350 degrees(F).
On a floured surface, roll the dough out to about 1/4-1/3 inch thick.
Cut out the cookies in any shape you want. Then take the scraps and press them back together and roll back out. Then cut more cookies. You should get around 2 dozen, depending on the size of the cookie cutter, you may get about 18 if you are using a large cookie cutter.
Place each cookie on a large sheet pan lined with parchment paper. About an inch or so apart, They don't spread much.
Bake for 8-10 minutes, you may need to do in batches or use two sheet pans at once.
Let the cookies cool completely. In the meantime, make the frosting.
Beat together the vegan butter and vegetable shortening with a whisk attachment. Until fully combined and fluffy.
Add the vanilla, then the powdered sugar a little at a time, until it has been fully incorporated. Add a pinch of salt, and combine.
Once the cookies are cool, spread a good layer of frosting on each cookie. Sprinkle a generous layer of cane sugar on top of the frosting then using your kitchen torch, caramelize all the sugar on top.
I usually keep them in the fridge until I serve them.