Lightly spoon flour into dry measuring cups and measuring spoons; level with a knife. Combine flour and the next 4 ingredients (through salt) in a medium bowl, stirring well with a whisk. Cut in butter with a pastry blender or 2 knives until mixture resembles coarse meal. Combine 1/3 cup ice water and vanilla; drizzle over flour mixture, 1 tablespoon at a time, tossing with a fork until moist. Place dough on plastic wrap; shape dough into a 12-inch log. Wrap tightly in plastic wrap; chill at least 1 hour or until dough is firm.
Preheat oven to 350°.
Unwrap dough log. Cut dough log into 24 (1/2-inch-thick) slices; place slices 2 inches apart on baking sheets lined with parchment paper. Bake at 350° for 15 minutes or until cookies are set. Cool cookies on pans 5 minutes. Remove cookies from pans, and cool completely on wire racks.