1. Preheat oven to 350°.
2. Lightly spoon flours into dry measuring cups; level with a knife. Combine flours, 3/4 cup powdered sugar, cornstarch, and salt in a food processor; pulse to combine. With food processor on, add butter through food chute a few pieces at a time; process 1 minute or until mixture is the texture of sand.
3. Combine 3 teaspoons ice water and vanilla in a small bowl. With food processor on, slowly add ice water mixture through food chute; process 1 minute or until very well combined. (Mixture will remain crumbly.) Add cherries and pistachios; pulse 10 times or just until combined. Transfer mixture to a bowl. (Mixture will be crumbly.) Gently press mixture into a level tablespoon; pack lightly with the heel of your hand. Turn out onto a baking sheet coated with cooking spray. Repeat with remaining dough to form 32 cookies.
4. Bake at 350° for 15 minutes or just until bottoms are golden. Remove from oven; cool 10 minutes on baking sheet.
5. Place remaining 1/2 cup powdered sugar in a large bowl. Add cooled cookies; toss gently to coat with powdered sugar. Transfer cookies to wax paper to cool completely.