In a medium-sized mixing bowl, mix flour, brown sugar, oats, cinnamon, and ginger.
Add melted butter and mix thoroughly until you have a bowl of small crumbs.
Using a melon baller or spoon, scoop out a little bit of the center of each peach half to increase the size of the hole the crumb filling will go into.
Place the cut peaches into a greased baking dish, individual ramekins, or muffin tins.
Stuff each peach half with crumbs.
Sprinkle remaining crumbs on top of each peach half.
Bake for 25 to 30 minutes or until the crumbs have browned and the peaches are soft but not falling apart.
Serve hot, topped with whipped cream or ice cream.
Video
Notes
Choose the best-tasting peaches. If your peach doesn't taste great before you bake it, it won't be the best baked peach, either.
Experiment with other spices in the crumb topping. I use cinnamon and ginger, but cardamom, allspice, and cloves would also be wonderful.
Put the peaches in the oven while you are eating dinner so they are ready just in time for dessert.
Store uneaten baked peaches in the refrigerator for up to 4 days and reheat in the microwave for about 30 seconds each before serving.