For Cookies:
Preheat oven to 350 degrees.
In a standing mixer or large bowl cream together butter, oil, 1 cup granulated sugar and powdered sugar for 2 minutes on medium speed.
Add in milk and eggs and mix until well combined.
In a separate medium bowl whisk together baking powder, cream of tartar, salt and flour.
Slowly add in a little flour mixture while beating and mix until just combined. Do not over beat.
In a small bowl pour in remaining 1/2 cup sugar.
Scoop 2 TBSP of dough into our your hand and form a ball.
Roll dough balls into sugar and place 12 to a cookie sheet.
Using a flat bottomed glass, press down on each ball until they are about 1/4 inch thick. The edges will become cracked.
Bake for 8 minutes and cool on a cookie wrack.
For Frosting:
Spoon frosting into a medium microwave proof bowl.
Heat for 20-30 and stir.
Divide frosting between a few bowls. The number of colors will determine how many bowls you will need.
Add a drop or two of food coloring to each bowl and stir to combine.
Pour frosting into piping bag, snip the tip off and drizzle over cookies.