Instructions

for the pie dough

Combine 1½ cups (210 grams) superfine brown rice flour, ½ cup plus 1 tablespoon (100 grams) potato starch, ¾ cup plus 2 tablespoons (100 grams) tapioca starch, 1 tablespoon sugar, 1 teaspoon xanthan gum, and ¾ teaspoon table salt in large bowl. Add 16 tablespoons unsalted butter, cut into 1-inch pieces and chilled, and 8 ounces cream cheese, cut into 1-inch pieces and chilled. Using your fingers, flatten butter and cream cheese into flour, creating large shards, until mixture feels very flaky. Add 7 tablespoons ice water and 1 teaspoon cider vinegar and, using your hands, work dough together, pressing until it comes together. (Dough may appear dry at first; continue working until it sticks.) If dough feels dry, add extra ice water, 1 teaspoon at a time, up to 3 teaspoons. Dough should mostly stick together with some smaller pieces falling off.
Transfer to counter and knead until dough comes together; distinct pieces of butter and cream cheese should remain visible. Divide dough in half and wrap each half in parchment paper. Press each into disk. Refrigerate for at least 45 minutes. (Dough can be refrigerated for up to 3 days.)

for the filling

Cook 2 pounds frozen sliced peaches in large Dutch oven over medium heat until thawed and beginning to soften, about 5 minutes. Add 2⅓ cups blackberries, ½ cup sugar, 1 tablespoon lemon juice, and ¼ teaspoon salt and cook, stirring occasionally, until fruit releases its juices and mixture comes to simmer, about 5 minutes.
Whisk 3 tablespoons cornstarch and 2 tablespoons water together in small bowl until smooth. Stir slurry into simmering fruit and cook, stirring constantly, until filling thickens and becomes glossy, 1 to 2 minutes. Transfer filling to shallow dish and let cool completely, about 1½ hours. (Cooling is essential so that filling sets and does not soften crust during assembly.)
Adjust oven rack to lower-middle position, place pizza stone on rack (optional; see headnote), and heat oven to 425 degrees.
Dust counter and rolling pin with tapioca starch. Roll 1 dough disk into 13-inch circle, ⅛ to ¼ inch thick. (If dough cracks, pinch back together.) Line bottom of 9-inch metal pie plate with dough, leaving ½-inch overhang; trim excess. (Reserve scraps in refrigerator for another use.) Place plate in freezer for 5 minutes to chill dough. 
Transfer cooled filling to pie plate and dot with 2 tablespoons unsalted butter, cut into ¼-inch pieces.
Roll second dough disk into 13-inch circle. Using 1-inch cutter, cut out shapes, leaving 3 inches between cutouts. Brush edges of bottom crust with 1 large egg, lightly beaten. Lift dough and place over filling. Press gently where top and bottom crusts meet. Trim excess. Brush top of dough with beaten egg. If desired, line rim of pie with cutouts.
Place plate on rimmed baking sheet and set on preheated pizza stone, if using. Bake for 15 minutes. Reduce oven temperature to 375 degrees and continue to bake until top is golden brown and filling is bubbling, 45 to 50 minutes longer.
Let pie cool for 1 hour before slicing and serving. (Pie can be refrigerated, covered, for up to 3 days.)