Stir together flour, baking powder and salt in a small bowl.
Beat butter, sugar, egg and vanilla in clean bowl until blended. Stir in flour mixture. Gather into ball. Wrap and refrigerate several hours or overnight.
Heat oven to 350 degrees F. Lightly coat baking sheets with nonstick vegetable-oil cooking spray.
Roll out. Add 1/4 cup each flour and toasted sesames seeds to the flour mixture in Step 1. Roll 2 teaspoonfuls dough into ball for each cookie; roll in more toasted sesame seeds. Flatten slightly; place glacéed cherry half in center of each. Bake 12 to 14 minutes, until lightly firm. Makes about 4 dozen cookies.