Preheat oven to 350 F. Line 3 baking sheets with parchment paper.
Using an electric mixer, beat butter and 1 cup powdered sugar in large bowl until light and fluffy. Mix in vanilla and salt, then pistachios and cherries. Stir in flours, do not overmix.
Working with one baking sheet at a time, shape dough into tablespoon sized balls and place on prepared sheet, spacing 1 inch apart.
Bake until bottoms just begin to turn golden brown, 15-16 minutes. Let cool on sheet 10 minutes. Repeat with remaining dough.
Meanwhile, place remaining powdered sugar in medium bowl. Working with 5 or 6 warm cookies at a time, gently coat in sugar. Transfer cookies to a piece of parchment paper to cool completely. Repeat with remaining cookies.