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 rack.

Cream together butter, powdered sugar and vanilla together until smooth.

Mix in puree and sour cream and mix until well blended.

Frost each cookie with about 1 tablespoon of frosting and chill cookies until ready to serve.