Preheat the oven to 350°F. Line two baking pans with silicone mats or parchment paper.
Combine the flour, baking soda, baking powder, and salt in a large bowl and whisk to mix. Put aside. Whisk the buttermilk and vanilla together in a small dish. Put aside.
Beat the sugars and shortening on medium speed in the bowl of a stand mixer with the paddle attachment until frothy, scraping down the sides as needed.
One by one, add the eggs, mixing just until combined, and then turn the speed down to medium-low.
Slowly pour in the buttermilk mixture after scraping down the sides. Three additions of the flour mixture should be made after lowering the mixer to low. Just until there are a few flour streaks left, scrape down the sides and continue to mix for a few more seconds.
Line the baking sheets with 2 tablespoons of dough, separating them by 2 inches, and bake for 9 to 11 minutes, or until the edges are golden brown. Let cool on the baking sheet for 10 minutes, then move to a cooling rack to cool completely. Repeat with the remaining dough.
In a small saucepan, melt the butter and brown sugar over low heat, stirring constantly, then stir in the milk and salt. Take off the heat and add the powdered sugar, about 2 tablespoons at a time, until the mixture achieves a spreadable consistency. Allow to cool until thickened, then decorate the cooled cookies as you think fit.