For the crust: Pulse the flour, sugar and salt together in a food processor. Add the butter and pulse until the mixture resembles a coarse meal. Add the water and pulse until the dough comes together. Turn the dough out onto a piece of plastic wrap, form into a disk and wrap well. Refrigerate until firm, at least 1 hour and up to 1 day.
Put the dough on a lightly floured piece of parchment paper and roll out to a 12-inch round. Refrigerate until firm, about 20 minutes.
Preheat the oven to 425 degrees F.
For the filling: Combine the rhubarb and butter in a skillet over medium heat. Saute until the rhubarb is slightly softened, about 3 minutes. Toss with the sugar. Put the strawberries in a bowl and add the softened rhubarb. Sprinkle the cornstarch over top and toss together.
Put the parchment paper with the dough on a flat baking sheet or on the underside of a rimmed baking pan. Spread the filling out on the dough, leaving a 1 1/2-inch border, then flip the edges over the filling. Beat the egg with 1 tablespoon water in a small bowl. Brush the crust lightly with the egg wash.
Bake until the crust is golden brown, 30 to 40 minutes. Cool on the baking sheet, then carefully transfer to a serving plate.