In a large mixing bowl, stir together the flour, cream of tartar, baking soda and salt. Using a pastry blender or 2 knives, cut in butter till the mixture resembles coarse crumbs.
In a small bowl, combine eggs, sugar and vanilla. Stir into flour mixture till well mixed. Form Dough into a ball. Place dough on a lightly floured surface. Knead for 12 to 15 strokes or until nearly smooth. Divide dough into three portions. Cover and chill in the refrigerator for 3 hours or till dough is easy to handle.
On the lightly floured surface, roll one portion of the dough at a time to 1/4-inch thickness. Using a 2-1/2-inch cookie or biscuit cutter, cut dough into desired shapes. Place 1 to 2 inches apart on ungreased cookie sheet.
Bake in a 350 degree F oven for 6 to 8 minutes or till edges are firm and bottoms are very lightly browned. Cool on cookie sheet for 1 minute. Transfer cookies to a wire rack; cool. Makes about 48 (2-1/2-inch) cookies.
Bake and cool cookies as directed. Place cookies in airtight container with waxed paper between layers. Seal, label, and freeze up to 1 month. Thaw 1 hour at room temperature before serving.