In an electric mixer, blend on medium speed butter, Greek yogurt, sugars, confectioners' sugar, egg yolks and one teaspoon of vanilla. Blend well.
Add slowly flour and salt.
Chill 2 hours. Roll out to 1.4 inch thick. Chill 30 minutes. Using a 2-3 inch round cookie cutter cut out shapes. Place 2 inches apart. Bake at 350, 8-10 minutes. Cool on a cooling rack.
Icing:
In a small bowl, combine confectioners' sugar, milk, and vanilla until smooth and glossy. Add 1 teaspoon at a time more milk if needed.
Divide into separate bowls, and add food coloring's to desired color. Place each individual color into a Ziploc bag. Snip end to 1/16 inch and different areas outline image then fill in each color. Repeat for each color.