Preheat oven to 350 degrees.
In a large mixing bowl, cream butter and sugar. Add brown sugar, vanilla, applesauce, and beat for 1-2 minutes.
Mix flour, arrowroot, salt, baking soda and baking powder together, and then sift dry ingredients over butter and sugar mixture. Mix just until incorporated. Add almond milk and mix until soft dough is formed, and cover and freeze dough for 15 minutes.
Use small ice cream scoop chilled dough and roll into balls, and arrange cookies on a clean baking sheet 2 inches apart to allow for spreading.
If you’ve rolled the dough into balls, dip a glass into cane sugar and gently smash down into a disc to help them cook more evenly. Sprinkle lightly with remaining cane sugar.
Bake on the center rack for 10-12 minutes for or very slightly golden brown.
Remove from oven and let rest on pan for a few minutes, then transfer to a cooling rack to cool completely.