Preheat oven to 375°. Stir together first 3 ingredients.
Split vanilla bean; scrape seeds into bowl of a heavy-duty electric stand mixer. Add butter and 1 cup sugar; beat at medium speed 2 minutes or until creamy. Add flour mixture; beat until blended.
Line bottom and sides of a 13- x 9-inch pan with parchment paper, allowing 2 to 3 inches to extend over sides; lightly grease parchment paper. Press dough into bottom of prepared pan. Bake at 375° for 20 minutes or until edges are golden brown.
Meanwhile, stir together corn syrup, 1/4 cup water, and remaining 1 cup sugar in a small saucepan over high heat, stirring just until sugar dissolves. Cook, without stirring, until a candy thermometer registers 250° (7 to 8 minutes).
While syrup cooks, beat egg whites at medium speed, using whisk attachment, until foamy.
When syrup reaches 250°, beat egg whites at medium-high speed until soft peaks form. While mixer is running, gradually add hot syrup to egg whites. Increase speed to high; beat until stiff peaks form. (Mixture should still be warm.) Add vanilla and peppermint extracts, and beat at medium speed just until combined. Fold in 1/2 cup peppermint candies.
Working quickly, spread mixture on warm cookie base, using a butter knife or offset spatula. Sprinkle with remaining 1/4 cup crushed peppermints, and cool.
Lift mixture from pan, using parchment paper sides as handles; cut into 32 bars.