01 - Whisk together flour, sugar, and salt in a large bowl. Cut in cold butter using a pastry blender or fingertips until mixture resembles coarse crumbs. Gradually add ice water, 1 tablespoon at a time, mixing until dough just comes together. Divide dough in half, shape into disks, wrap in plastic, and chill for at least 1 hour.
02 - Combine strawberries, rhubarb, sugar, cornstarch, cinnamon, salt, vanilla, and lemon juice in a large bowl. Toss gently to coat and set aside.
03 - Preheat oven to 400°F. Roll out one dough disk on a floured surface to fit a 9-inch pie pan. Line pan with dough, trimming edges. Fill with strawberry-rhubarb mixture, spreading evenly.
04 - Roll out second dough disk and cut into 3/4-inch wide strips. Lay half the strips across the pie vertically, then weave remaining strips horizontally to form a lattice. Trim and crimp edges to seal.
05 - Whisk egg and milk together; brush over lattice crust. Sprinkle with coarse sugar if desired. Place pie on a baking sheet and bake for 20 minutes at 400°F. Reduce oven to 350°F and bake an additional 35-40 minutes, until crust is golden and filling is bubbling. Cool at least 2 hours before slicing.