Preheat your oven to 425°F (220°C).
In a large mixing bowl, combine the strawberries, rhubarb, sugar, flour, lemon juice, and vanilla extract. Stir until the fruit is evenly coated. Let the mixture sit for about 10 minutes to release juices.
Roll out one of the pie crusts and place it into the bottom of the pie pan, pressing it gently against the sides.
Pour the fruit mixture into the pie crust, spreading it evenly. Dot the top with small pieces of butter.
Roll out the second pie crust and place it over the filling. Trim any excess dough from the edges and crimp to seal the edges. Cut a few slits in the top crust to allow steam to escape.
In a small bowl, whisk together the egg and milk. Brush this mixture over the top crust for a nice finish.
Bake in the preheated oven for 10 minutes, then reduce the temperature to 350°F (175°C) and bake for an additional 35-40 minutes, or until the filling is bubbly and the crust is golden brown.
Remove the pie from the oven and let it cool for at least 2 hours before slicing.