1. Peel, core, and cut up the apples.
2. Peel and cut up the peaches.
3. Marinate fruit in rum, cinnamon, nutmeg, ginger, and 1 brown sugar. Let sit for about 2 hours.
4. Prepare piecrust: Measure flour, sugar, and a generous pinch of salt into a food processor fitted with a metal blade. Pulse once or twice to mix. Add butter and pulse on and off until mixture resembles small peas. Add ice water all at once. Pulse a few more times, just until dough starts to come together. Turn dough onto counter and flatten into a disk. Wrap dough well in plastic or waxed paper, and refrigerate for at least 30 minutes before rolling out.
5. Drain fruit and place in crust fitted into deep dish. Add top crust and slash top. Brush with milk and bake 10 minutes at 425 degrees F. Finish baking at 350 degrees F for around 35 minutes. Instead of discarding marinade, thicken it slightly and serve over ice cream.