To prepare the cookies:

1. In a large bowl, cream the butter and sugar together on medium speed until light and fluffy, about 3 minutes. Add the egg and vanilla extract, stirring on medium for another minute. Add the flour, salt, cream of tartar, and baking soda, stirring on low just until combined. Use a small cookie scoop to portion out 2-teaspoon sized rounds of dough. Roll them quickly to make them round and then roll each dough ball in in the colored sugar. Place on a parchment paper lined baking sheet and refrigerate until firm, about 30-45 minutes.
2. When ready to bake, preheat the oven to 350 degrees. Bake the cookies for about 10 minutes or until the edges are barely beginning to set. The cookies will appear slightly underdone. Allow to cool completely prior to filling each with the frosting.

To prepare the frosting:

1. Combine all of the ingredients in a large bowl and stir on medium until it smooths into a fluffy frosting. Add a teaspoon or two of extra milk as needed to thin out the frosting. Sandwich the cookies with frosting and enjoy!