Prepare the crust: In a large mixing bowl, whisk together the brown rice flour, sorghum flour, tapioca starch, psyllium powder, coconut sugar, and salt. Cut in the chilled vegan butter until the mixture resembles coarse crumbs with some pea-sized pieces remaining.

Bring the dough together: Mix the vinegar into 10 tablespoons ice water. Drizzle into the flour mixture, tossing gently. Add additional water, 1 tablespoon at a time, only until the dough holds together when pressed. Divide into two disks, making the bottom-crust disk slightly larger. Wrap and refrigerate for 1 hour.

Prepare the peaches: Place the sliced peaches in a large bowl with coconut sugar, lemon juice, and salt. Toss gently and let stand for 25–30 minutes, allowing the peaches to release some of their natural juices.

Create the rosemary-vanilla syrup: Strain the peaches over a saucepan, reserving all the juice. Add the rosemary sprig to the liquid and simmer gently for 2–3 minutes. Remove and discard the rosemary, then continue simmering until the juices reduce to approximately 3–4 tablespoons of fragrant syrup. If the peaches release very little liquid, simply warm it with the rosemary rather than reducing it excessively. Remove from the heat, stir in the vanilla, and cool for 10 minutes.

Finish the filling: Toss the drained peaches with the white rice flour, cornstarch, and lemon zest until evenly coated. Fold in the cooled syrup. The peaches should look glossy and lightly coated, without a pool of thin liquid.

Prepare the pie plate: Preheat the oven to 425°F (220°C). Roll the larger dough disk between two sheets of lightly floured parchment into a circle approximately 12–13 inches wide and 1/8 inch thick. Carefully transfer to a standard 9-inch pie plate and press gently into the bottom and sides. Refrigerate while preparing the top crust.

Assemble the pie: Spoon the filling into the crust, mounding it slightly in the center. Roll the remaining dough and cut into wide strips for a lattice, or leave it whole for a traditional top crust. Cover the filling, trim and seal the edges, and crimp. If using a solid top crust, cut several steam vents.

Add the finishing touch: Combine the plant-based milk and maple syrup. Lightly brush over the exposed pastry and sprinkle with coconut sugar, if using. Chill the assembled pie for 15 minutes.

Bake until golden: Place the pie on a rimmed baking sheet on the lower oven rack. Bake for 20 minutes at 425°F, then reduce the temperature to 375°F (190°C). Continue baking for 40–50 minutes, until the crust is deeply golden and the peach filling bubbles thickly near the center. Shield the crust edges with foil if they brown too quickly.

Let the filling settle: Transfer the pie to a cooling rack and let it cool for at least 3 hours before slicing. This allows the filling to thicken so that the tender peaches remain nestled together rather than spilling onto the plate.