Place butter into the bowl of a stand mixer. Beat on medium speed for 2 minutes, until light and fluffy. Add cream cheese and beat another 2 minutes. Slowly add sugar, beating another 2 minutes. Reduce speed to low and add egg yolks one at a time then vanilla extract. Turn mixer off for a minute. Mix flour and salt in large mixing bowl. Turn mixer back on low speed and add 1/3 of flour mixture beating until combined. Add the next 1/3 of flour mixture beating until combined, then the final 1/3 flour mixture. Mix until just combined. Transfer dough to a lightly floured counter top or on top of floured parchment paper. With floured hands, knead a few times folding dough in half then pressing and in half again. Divide dough into 2 equal parts forming discs. Wrap each disc with plastic wrap and refrigerate 2 hours before using or freeze for 45 minutes-1 hour before using.
When dough has been chilled, roll dough into 1/4-1/2 inch thick large round onto a lightly floured counter top. Preheat oven to 350 degrees F. Use cookie cutters to cut desired cookie shapes and transfer to baking sheets. Cookies can be close to each other. Very minimal spreading. Bake cookies for 15 minutes, until lightly golden on edges. Let cool completely before icing.
To prepare icing place powdered sugar into a medium mixing bowl. Stir in milk until smooth then add corn syrup beating until smooth. Divide icing into bowls and add food coloring as desired. Dip or paint cookies with a brush. Let dry completely before packaging.