To prepare the cookies:

1. In the bowl of a stand mixer or a large mixing bowl, combine the butter and sugar, creaming on medium speed until the mixture is light and fluffy, about 2 minutes. Add the eggs, vanilla, and milk, and stir to combine for an additional 30 seconds. Scrape the sides of the bowl.
2. In a separate bowl, combine the flour, cream of tartar, baking soda, and salt. Add the dry ingredients to the butter mixture and mix slowly until well incorporated. Scrape the sides of the bowl as needed.
3. Divide the dough into two flat rounds and wrap in plastic wrap. Chill in the fridge for at least 1 hour or up to 3 days.
4. When ready to bake, preheat the oven to 350 degrees and prepare two pans by lining them with a sheet of parchment paper or silicone baking mats. Generously flour a work surface and roll one round of dough out to 1/8-1/4” thick using a floured rolling pin. Use medium-sized cookie cutters to cut out shapes of dough and place them 2” apart on the prepared pans. Place the whole pan in the freezer for 5 minutes (or fridge for 10) to set the shaped dough and then bake in the oven for about 10 minutes, or until the edges of the cookies are well-set. Allow to cool on the pan briefly and then remove to a cooling rack to cool completely. Repeat this process with the remaining dough. Try not to get the dough too-floured or overworked as this can change the texture of the cookies. If your dough gets too warm or sticky, place back in the fridge to chill a bit.

To prepare the frosting:

1. In a large bowl, combine the butter, sugar, egg, vanilla, and salt, mixing until well combined. Add milk by the tablespoon until the frosting is thick but smooth, similar to the consistency of a thick cake buttercream. Use gel food coloring to dye the frosting and a knife to spread the frosting on the cookie. Enjoy!