Preheat oven to 300ºF. In a large mixing bowl, beat ½ cup softened butter and ½ cup shortening with an electric mixer on medium to high speed for 30 seconds. Add 2 cups sugar, 1 tsp baking soda, 1 tsp cream of tartar, and a pinch of salt. Beat mixture until combined, scraping sides of bowl occasionally. Beat in 3 egg yolks and ½ tsp vanilla. Beat in as much of the 1¾ cups flour as you can with the mixer. Stir in any remaining flour.
Shape dough into 1-inch balls. Place balls 2 inches apart on ungreased cookie sheets. Bake for 12 to 14 minutes or until edges are set; do not let edges brown. Cool cookies for 2 minutes on cookie sheet. Transfer cookies to wire racks and let cool.
Tender and sweet sugar cookies offer welcome canvases for flavor artistry. Add dashes of new flavors -- spices, shredded citrus peel, or extracts -- to make your cookies distinct.
Layer cookies between waxed paper in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months.