In a large bowl, mix flour, salt, and sugar. Cut in cold butter with a pastry cutter or fork until the mixture resembles coarse crumbs.
Add ice water one tablespoon at a time, mixing until the dough just comes together.
Divide the dough in half, shape each half into a disc, wrap in plastic, and chill for at least 1 hour.
In a large bowl, toss rhubarb, strawberries, granulated sugar, brown sugar, cornstarch, salt, lemon juice, and vanilla extract. Let sit for 10–15 minutes.
On a lightly floured surface, roll out one dough disc and fit it into a 9-inch pie pan. Trim excess dough from edges.
Pour the fruit filling into the crust and dot with small pieces of butter.
Roll out the second dough disc and place it over the filling, or cut into strips for a lattice top. Trim and crimp the edges.
Brush the top crust with beaten egg and sprinkle with coarse sugar, if using.
Chill the assembled pie in the fridge or freezer for 15 minutes to help the crust hold its shape during baking.
Preheat the oven to 400°F (200°C). Place the pie on a baking sheet to catch drips and bake for 20 minutes.
Reduce heat to 350°F (175°C) and bake for an additional 35–40 minutes until crust is golden and filling is bubbling.
Let the pie cool completely for 2–3 hours before slicing to allow the filling to set.