Preheat oven to 350°. Line 3 baking sheets with parchment paper.
In a large bowl, beat butter and 1½ cups sugar with a mixer at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in vanilla.
In a medium bowl, whisk together Swans Down® Cake Flour, cream of tartar, baking soda, and salt. Gradually add flour mixture to butter mixture, beating until combined.
In a small bowl, stir together cinnamon and remaining 3 tablespoons sugar. Using a 1-inch spring-loaded ice cream scoop, scoop dough into mounds. Roll each mound into a ball, and roll balls in cinnamon-sugar mixture, coating completely. Place 2 inches apart on prepared pans.
Bake until edges are just beginning to brown, 8 to 10 minutes. Let cool on pans for 5 minutes. Remove from pans, and let cool completely on wire racks.
Makes 36 cookies