Make the crust by pulsing the gluten free flour, cold butter, sugar, salt, and xanthan gum in a food processor until the mixture resembles coarse crumbs. Drizzle in ice water one tablespoon at a time, pulsing until the dough just comes together. Shape into a disc, wrap in plastic, and refrigerate for 30 minutes.
Roll the dough out between two sheets of parchment paper into a 12-inch circle. Transfer to a 9-inch pie plate, pressing into the bottom and sides. Trim the edges and crimp decoratively. Refrigerate while you prepare the filling and topping.
Preheat your oven to 375 F. Gently toss the blueberries, raspberries, and blackberries together with the granulated sugar, cornstarch, lemon juice, and vanilla in a large bowl. Be careful not to crush the berries.
Make the crumble topping by combining the oats, almond flour, brown sugar, cinnamon, and salt. Add the cold butter and work it in with your fingers until you have chunky, clumpy crumbs.
Pour the berry filling into the chilled pie crust, mounding it slightly in the center. Scatter the crumble topping evenly over the berries, pressing it gently into clumps.
Place the pie on a rimmed baking sheet to catch drips. Bake for 50 to 60 minutes until the crumble is golden brown, the crust is deeply golden, and the filling is bubbling thickly around the edges. If the topping browns too quickly, tent loosely with foil.
Let the pie cool at room temperature for at least 3 hours before slicing. This resting time is essential for the filling to set properly.