Preheat oven to 350°F. Line a 9x13-inch baking pan with parchment paper and set aside.

In a large mixing bowl, beat softened butter and sugar until creamy. Add egg and vanilla extract, and mix well. Stir in baking soda, cream of tartar, and salt. Gradually add flour, mixing just until combined.

Press dough evenly into the prepared pan. Bake for 14-15 minutes until edges are golden. Let cool completely before frosting.

For the frosting, beat softened butter until smooth. Gradually add powdered sugar, vanilla, and enough milk until desired consistency is achieved. Tint frosting with food coloring if desired.

Spread frosting evenly over cooled cookie base. Decorate with sprinkles as desired. Cut into bars and serve.