Mix strawberries, rhubarb, brown sugar, white sugar, flour, cornstarch, cinnamon, and allspice together in a large bowl; stir until flour and cornstarch dissolve. Let filling stand for 30 minutes. Add an additional tablespoon of cornstarch if filling is very juicy.

Preheat oven to 400°F (200°C).

Roll 1 pie dough into an 11-inch circle on a floured work surface and line a 9-inch pie dish with the dough. Roll the remaining dough into a 10-inch circle and set aside.

Pour filling into the pie dish. Scatter diced butter over the top.

Cut the remaining crust into 3/4-inch wide strips and weave a lattice pattern over the filling. Use water to moisten the rim of the bottom crust for sealing. Press the lattice strips down and trim neatly. Brush crust with milk and sprinkle with white sugar.

Cover the pie edges with aluminum foil to prevent over-browning. Bake for 15 minutes at 400°F (200°C). Reduce temperature to 375°F (190°C) and bake for an additional 40 minutes, removing the foil 15 minutes before the end. Let pie rest in the turned-off oven with the door open for 15 minutes, then close the door and rest for another 15 minutes.