Whisk flour, salt, and sugar. Cut in cold butter until mixture looks like coarse crumbs with pea-sized butter pieces. Add ice water, 1 tbsp at a time, and form a dough. Divide into two discs, wrap, and chill for at least 30 minutes.
Combine strawberries, rhubarb, granulated sugar, brown sugar, cornstarch, lemon juice, vanilla, and cinnamon in a large bowl. Toss gently and let sit 10–15 minutes.
Preheat oven to 425°F (220°C). Roll one dough disc to fit a 9-inch pie pan, transfer, and trim. Fill with fruit mixture and dot with butter. Cover with top crust or lattice, seal edges, and brush with egg wash. Sprinkle coarse sugar if desired.
Bake at 425°F for 15 minutes, then reduce to 375°F (190°C) and bake for 35–45 minutes until crust is golden and filling is bubbling. Tent with foil if crust browns too quickly. Cool at least 2 hours before serving.
Notes
If fruit is very juicy, increase cornstarch by 1–2 tbsp.
To prevent a soggy bottom, place a baking sheet on the lower oven rack to help crisp the bottom crust.
Pie can be assembled and frozen unbaked for up to 3 months; bake from frozen, adding 10–15 minutes to baking time.