01 - In a large mixing bowl, whisk together the gluten-free flour blend, sugar, and salt until evenly distributed.
02 - Add the cold cubed butter to the flour mixture. Using a pastry blender or your fingertips, work the butter into the dry ingredients until the texture resembles coarse meal with some pea-sized pieces remaining.
03 - In a small bowl, beat the egg with 4 tablespoons of ice water. Gradually drizzle the egg mixture into the flour-butter mixture, stirring gently until the dough just begins to come together. Add remaining ice water 1 tablespoon at a time if the dough feels dry. Divide the dough into two equal portions, shape each into a flat disc, wrap tightly in plastic wrap, and refrigerate for at least 1 hour.
04 - Preheat the oven to 400°F. Position a rack in the lower third of the oven for optimal bottom-crust browning.
05 - In a large bowl, combine the sliced strawberries, diced rhubarb, granulated sugar, cornstarch, cinnamon, salt, and lemon juice. Toss gently but thoroughly until all the fruit is evenly coated and no dry cornstarch remains visible.
06 - On a lightly floured surface or between two sheets of parchment paper, roll out one disc of chilled dough to a 12-inch circle approximately ⅛ inch thick. Carefully transfer the dough to a 9-inch pie plate, gently easing it into the bottom and sides without stretching. Trim any overhanging dough to leave a 1-inch border.
07 - Pour the strawberry-rhubarb filling into the lined pie plate, mounding it slightly in the center. Spread evenly and press gently to eliminate large air pockets.
08 - Roll out the second disc of dough and drape it over the filling for a solid top crust, or cut into strips and weave a lattice pattern. Fold the top edge under the bottom crust edge and crimp firmly to seal. Cut several small vents in the top crust if using a solid lid. Brush the entire surface with beaten egg and sprinkle evenly with sugar.
09 - Place the pie on a rimmed baking sheet to catch any drips. Bake at 400°F for 45 to 50 minutes, until the crust is deep golden brown and the filling is bubbling visibly through the vents. Tent loosely with aluminum foil if the crust browns too quickly.
10 - Transfer the pie to a wire cooling rack and allow it to cool for at least 2 hours before slicing. This resting time allows the filling to set properly. Serve warm or at room temperature.