01 - Whisk together flour, sugar, and salt in a large bowl. Cut cold butter into the mixture using a pastry blender or fingertips until coarse crumbs form. Gradually add ice water 1 tablespoon at a time, mixing until dough holds together. Divide dough in half, form into disks, wrap in plastic, and refrigerate for 1 hour.
02 - Combine strawberries, rhubarb, sugar, cornstarch, cinnamon, salt, vanilla, and lemon juice in a large bowl. Toss gently until fruit is evenly coated. Set aside while preparing crust.
03 - Preheat oven to 400°F. Roll out one dough disk on a floured surface to fit a 9-inch pie pan. Transfer dough to pan, pressing into bottom and up sides. Trim edges evenly.
04 - Pour strawberry-rhubarb mixture into prepared crust, spreading evenly. Roll remaining dough disk and cut into 3/4-inch wide strips. Weave strips across pie in a lattice pattern, alternating vertical and horizontal placement. Trim edges and crimp to seal bottom and top crusts.
05 - Whisk egg with milk until blended. Brush mixture evenly over lattice crust. Sprinkle with coarse sugar if using. Place pie on baking sheet and bake at 400°F for 20 minutes. Reduce temperature to 350°F and bake 35–40 minutes longer until crust is golden brown and filling bubbles. Cool completely for 2 hours before slicing.