Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking soda, and salt, stirring well with a whisk.
Place granulated sugar and butter in a large bowl; beat with a mixer at medium-high speed until light and fluffy (about 1 minute). Add vanilla and egg whites, beating until well blended. Beating at low speed, gradually add flour mixture, beating just until a soft dough forms. Divide dough into 2 equal portions. Place each portion on plastic wrap; shape each portion into an 8-inch log. Wrap logs in plastic wrap; freeze at least 2 hours or until very firm.
Preheat oven to 375°.
Working with one dough log at a time, lightly coat each log with cooking spray. Roll each dough log in sugar sprinkles, pressing gently to adhere. Cut each dough log into 32 (1/4-inch-thick) slices; place 1 inch apart on baking sheets coated with cooking spray. Bake at 375° for 10 minutes or until set. Remove from pans; cool completely on wire racks.