Preheat oven to 425°F. Mix the sugar and cornstarch, then lightly stir together the strawberries and rhubarb. Set aside while you make the pie crust (unless you’re using purchased pie crusts).
Mix together the flour, sugar, and salt. Add the shortening and work with a fork until it forms pea-sized crumbs. Transfer the dough to a large bowl and let sit. In a small bowl, whisk together the egg, vinegar, and water. Pour over the dough and mix until combined (dough will be sticky). Cover with plastic wrap and chill in the refrigerator for at least 1 hour before rolling.
Divide the chilled dough in half on a generously floured work surface. Roll half of the dough to ¼-inch thickness and transfer to a 9-inch pie dish. Pour in strawberry-rhubarb filling. Dot with butter. Top with crust. Flute edges and cut slits in top. Bake 40 to 50 minutes, or until the crust is nicely browned and juice begins to bubble through slits in pie crust. Best if served slightly warm. Serves eight.