Whisk together flour, salt, and sugar in a large bowl. Cut in cold cubed butter using a pastry cutter until the mixture resembles coarse, pea-sized crumbs.
Drizzle in ice-cold water one tablespoon at a time, stirring gently until the dough just holds together. Divide into two flat discs, wrap in plastic wrap, and refrigerate for at least 1 hour.
Combine rhubarb, strawberries, sugar, cornstarch, lemon juice, vanilla extract, cinnamon, and salt in a large bowl. Toss gently to coat and let the mixture sit for 15 minutes to macerate.
Preheat oven to 425°F (220°C) with a baking sheet on the lower rack. Roll out one dough disc into a 12-inch circle and fit it into the pie dish without stretching, letting the edges overhang.
Roll out the second dough disc into a 12-inch circle. Keep it whole for a full top crust, or cut into ½–¾-inch strips for a lattice top. Refrigerate until ready to use.
Pour the filling into the unbaked shell and dot with small pieces of cold butter. Top with the second crust or weave the lattice, then trim edges to a 1-inch overhang, fold under, and crimp to seal. Cut steam vents if using a full top crust.
Whisk together the beaten egg and heavy cream, then brush the mixture evenly over the top crust and crimped edges. Sprinkle generously with coarse or turbinado sugar.
Bake at 425°F for 20 minutes, then reduce heat to 375°F (190°C) and continue baking for 35–40 more minutes, until the crust is deep golden and the filling is actively bubbling. Shield the edges with foil if they brown too quickly.
Transfer the pie to a wire cooling rack and allow it to cool for at least 3–4 hours before slicing. This allows the filling to fully set and ensures clean, beautiful slices.