Preheat oven to 350 degrees F. Line 8” square with parchment paper.
Mix together sugar cookie dough, flour and buttermilk in a large bowl. Stir in red food coloring.
Press dough into the prepared pan. Bake for 13 to 14 minutes are until edges start to brown. Remove from oven.
In medium bowl, beat cream cheese, butter, milk and 1 teaspoon vanilla with electric mixer on low speed until smooth. Gradually beat in powdered sugar, 1 cup at a time, on low speed until smooth and spreadable. Frost cake. Store covered in refrigerator.