Pulse flour, 1 tbsp sugar, and salt in a food processor. Add cold butter and pulse until pea-sized bits remain. Drizzle in ice water until the dough just holds together; divide into two discs, wrap, and chill at least 30 minutes.

Toss rhubarb, strawberries, 3/4 cup sugar, cornstarch, lemon juice, vanilla, and salt in a large bowl; let sit 20 minutes, stirring once or twice.

Roll one dough disc to a 12-inch circle. Fit it into a 9-inch pie plate, leaving the overhang.

Scrape the fruit and all its juices into the crust. Dot with 1 tablespoon cold butter. Roll the second disc to a 12-inch circle, place on top, trim the overhang to 1/2 inch, fold under, and crimp. Cut vents, brush with egg wash, and sprinkle with coarse sugar.

Bake at 400°F (200°C) for 20 minutes, then reduce to 350°F (175°C) and bake 40 to 45 minutes until deep golden and thickly bubbling.

Cool completely on a wire rack, at least 4 hours, then slice and serve.