Preheat oven to 375℉. Line two baking sheets with parchment paper and set aside.
In a large bowl, whisk together flour, sugar, baking powder, and salt. Grate butter and add to bowl to combine more easily. Using fingers, rub in butter with ingredients until mixture becomes coarse. A pastry cutter also works for this step.
Fold in blueberries and peaches.
In a small bowl, add buttermilk, egg, and vanilla and whisk together until well combined.
Pour into flour mixture and mix together using a fork until dough starts to come together. It's okay for some flour to be left in bowl.
Transfer dough to a floured surface and knead a couple times just until remaining flour becomes incorporated into dough.
Gently pat dough into a 1 inch thick round. Cut dough evenly into 12 different wedges or squares.
Transfer to prepared baking sheets.
Brush with buttermilk.
Bake until golden brown, 18-23 minutes.
Cool on wire racks.