Add the flour, baking powder, baking soda, spices, and salt to a mixing bowl. Whisk the dry ingredients together and set aside for now.
Cut the cold butter into 12 chunks. Beat the butter and brown sugar together on medium speed until the butter and sugar are blended together and there are no more obvious chunks of butter left.
Add the molasses, vanilla, applesauce, and milk to the creamed butter mixture. Beat on medium-low speed just until evenly blended. Scrape down the bowl and the beaters, keeping all the scrapings in the bowl. The mixture may look curdled and that’s ok.
Add 1/3 of the flour mixture and mix on low speed just until incorporated. Repeat, then scrape down the bowl and beaters again, keeping all the scrapings in the bowl. Use a sturdy spatula to fold in the last of the dry ingredients.
Divide your dough in half and flatten each piece into a 1” thick disc. Wrap both pieces in plastic wrap, place them in a ziplock bag, and chill for at least three hours. After the chilling time, you can freeze the dough for several months as long as it is tightly wrapped in plastic wrap and stored in a ziplock bag.
Preheat your oven to 375 degrees.
Roll out one piece of your chilled dough to 1/8” thick between two pieces of waxed paper. Several times as you are rolling, gently peel off the top piece of waxed paper then place it back on the dough and flip the dough over. Gently peel off what is now the top piece of waxed paper then place it back on the dough and keep rolling the dough out. (This extra step prevents wrinkles in the waxed paper and in your dough.)
Once the dough is fully rolled out, slide the dough (still sandwiched between the two pieces of waxed paper) onto a cookie sheet and place in the freezer for 15 minutes.
Use cookie cutters to cut out your dough. You can use any size cutters you like, but be sure to only bake cookies of the same size together on the same baking sheet. Place each cut out on a parchment-lined baking sheet. Re-roll the scraps and chill the rolled out dough as directed above. After rolling, chilling, and cutting two times, save the remaining scraps to combine with those from the second piece of dough.
Repeat the above rolling, chilling, and cutting directions with the second piece of dough. Gather all of the remaining scraps together into a ball, roll out as directed above, chill the rolled out dough, and cut out more cookies. Repeat until all of the dough is used.
Bake cookies of the same size together. Bake tiny 1 1/2” tall cookies for seven minutes and larger 3 1/2” tall cookies for 10 minutes. Adjust the baking time for other sizes accordingly. Ovens vary, so these times are approximate. These cookies should be crisp all the way through once they have cooled. If your first pan of cookies is still soft when cooled, you need to bake the next batch a little longer. If your edges are too well done, you need a shorter baking time.
Let your cookies cool fully on the pan before decorating them. Once the icing if fully dry, store the cookies in an airtight container for up to a week. I recommend placing a piece of waxed paper between the layers of cookies.