Prepare the double-crust pie dough and roll out one portion to line the base of a pie pan, reserving the second portion for the top crust. Combine the chopped rhubarb, prepared strawberries, granulated sugar, minute tapioca, flour, lemon zest, lemon juice, cinnamon, and vanilla in a large mixing bowl, then transfer this mixture to the lined pie dish. Cut the butter into small pieces and scatter evenly over the fruit filling. Roll out the reserved dough and lay it gently over the filling as a whole top crust with slits for venting or slice it into strips for a lattice arrangement. Press and crimp the edges to seal. In a small bowl, whisk the beaten egg with the teaspoon of water to create an egg wash; brush this over the top crust, then lightly sprinkle with extra sugar. Loosely shield the pie edges with foil and bake in a preheated oven at 425°F for 15 minutes, then reduce the temperature to 375°F and continue baking for an additional 45 to 50 minutes, or until the filling bubbles and the crust achieves a deep golden hue. Allow the pie to cool for a minimum of 2 hours before slicing and serving.