Preheat oven to 350 degrees. Line a large baking sheet with parchment paper. Set aside.
In a large bowl, whisk together flour, cinnamon, nutmeg, allspice, ginger, baking powder, baking soda and salt.
In the bowl of a stand mixer fitted with a paddle attachment, beat butter and sugar on medium-high speed until light and fluffy, about 2-3 minutes. Add egg, applesauce and vanilla extract and continue to beat until smooth, scraping the sides of the bowl with a spatula, as needed. Reduce the speed to low and slowly add the flour mixture mixing until just incorporated. Do not overmix.
Scoop dough with a 1 1/2-inch cookie scoop and form into balls. Roll the balls in the pure cane sugar. Place on prepared sheet 2 inches apart. Flatten each cookie slightly with the bottom of a glass. Bake for 10-11 minutes until edges of cookies are set. Let cool slightly on sheet, then remove to wire racks. Repeat with remaining dough.
Store cooled cookies at room temperature in an airtight container for up to five days.