Preheat oven to 375°F. Combine flour, baking soda, and cream of tartar, stirring with a whisk. Combine 1 cup of sugar and butter in a large bowl, and beat with a mixer at medium speed until well blended. Add corn syrup, vanilla, and egg, beat well. Gradually add flour mixture to sugar mixture, beating just until combined. Cover and chill 10 minutes.
Combine 3 Tablespoons sugar and cinnamon stirring with a whisk. With moist hands, shape dough into 1-inch balls. Roll in the sugar mixture.
Place 2 inches apart on baking sheets coated with cooking spray. Flatten balls with a glass. Bake for 7-8 minutes.