Combine flour, sugar, and salt. Cut in cold butter, then add ice water until the dough comes together. Divide into two discs and chill for at least 2 hours.
Mix strawberries, rhubarb, sugars, cornstarch, lemon juice, vanilla, and salt in a large bowl. Let the filling rest for about 15 minutes.
Roll one dough disc into a 12-inch circle and place it into a 9-inch pie dish. Press gently without stretching the dough.
Pour the fruit filling into the bottom crust and spread it evenly. Add a few small pieces of butter on top if desired.
Roll out the second dough disc. Place it over the filling as a full crust with vents, or cut it into strips for a lattice crust.
Refrigerate the assembled pie for 15–20 minutes to help the crust hold its shape.
Brush the top crust with beaten egg and sprinkle with coarse sugar.
Bake at 400°F for 20 minutes. Then reduce the heat to 375°F and bake for another 35–45 minutes, until the crust is golden and the filling bubbles thickly.
Let the pie cool for at least 4–6 hours before slicing. For the cleanest slices, cool overnight.
