Add flour, salt, and sugar to a food processor and pulse to combine.

Add cold butter and pulse about 8–10 times, or until the mixture resembles coarse crumbs with visible butter pieces about the size of peas.

Drizzle in ice water 1 tablespoon at a time, pulsing just until the dough starts to clump together.

Turn the dough out onto a floured surface, divide in half, shape into discs, wrap in plastic wrap, and chill for at least 1 hour.

In a large bowl, toss the rhubarb and strawberries with the granulated sugar, brown sugar, and lemon juice. Let sit for 15–30 minutes to draw out excess moisture.

Drain the fruit using a strainer or colander, then return it to the bowl. Add the vanilla extract, salt, cornstarch, and quick-cooking tapioca. Stir well until everything is fully combined.

Roll out one disc of dough into a large circle and fit it into a 9-inch pie plate, leaving a little overhang.

Spoon the fruit filling into the crust and mound it slightly in the center.

Roll out the second disc into a rectangle and cut it into strips, about ½ to ¾ inch wide.

Lay half of the strips horizontally across the top of the pie, evenly spaced. Fold back every other strip halfway, then lay one strip vertically across the pie. Fold the horizontal strips back into place, then fold back the alternate strips and lay down the next vertical strip. Repeat until the lattice is complete.

Trim any overhanging strips to match the bottom crust, then fold the edges under and crimp with your fingers or a fork.

Whisk together the egg and water, then brush it over the lattice and edges. Sprinkle with coarse sugar if using.

Place the pie in the fridge for 15 minutes while the oven preheats to 400°F.

Set the pie on a parchment-lined baking sheet and bake for 20 minutes.

Reduce the oven temperature to 375°F and continue baking for another 40–50 minutes, until the crust is golden and the filling is bubbling.

If the edges start to brown too quickly, cover them loosely with foil or use a pie shield for the remainder of the bake.

Let the pie cool completely on a wire rack for at least 3 hours before slicing.