Place the vegan buttery spread and the brown sugar in a mixing bowl and mix on medium low speed until light and fluffy.
Add the molasses, applesauce, and vanilla, and mix on low speed to combine.
Add the dry ingredients and mix on low speed until combined.
Divide the dough into two balls and wrap in plastic wrap, then flatten into discs. Place in the refrigerator to chill for 2 hours.
Preheat the oven to 350 degrees F. Line a 2 cookie sheets with parchment paper.
Sprinkle gluten free flour on your rolling pin and rolling surface. I like to place parchment on the counter, then put flour on top of that. Unwrap a disc of dough and place on the floured surface.
Using a well-floured rolling pin, roll out the dough until it is ¼ inch thick.
Cut the dough into desired shapes. I used 2 inch round Linzer cookie cutters, but you can be creative! Hearts, stars, or trees would work well for sandwich cookies.
Bake at 350 degrees F for about 9-10 minutes. Don't overbake. If you use very large cookie cutters, the baking time may vary.
Let the cookies cool on the cookie sheet for a few minutes before moving to a wire rack to cool completely.
Repeat steps 7-10 with the other disc of dough.
Once the cookies are cool, make the frosting. Place the vegan buttery spread and one cup of powdered sugar in a mixing bowl and beat together.
Alternate adding more powdered sugar and non-dairy milk until the frosting is a thick, spreadable consistency.
Spread frosting on the underside of half of the cookies, then top with more cookies to make a sandwich.