Light charcoal briquettes in a campfire or outdoor charcoal grill; burn until coals are mostly covered in ash, 15 to 20 minutes.
Meanwhile, sift flour, baking powder, cinnamon, and salt together in a bowl. Stir in 1 1/2 cups sugar, then stir in milk until batter is well combined.
Toss peaches with remaining 1 1/2 cups sugar in a separate bowl; mix until evenly coated.
Rake coals into a flat bed; place a campfire-safe Dutch oven on top.
Add butter to Dutch oven until melted; swirl Dutch oven to coat all sides with melted butter. Pour batter into the pot, add peach mixture to center of the batter. Cover Dutch oven with the lid; place hot charcoal on top of lid.
Cook until done, about 1 hour, checking every 20 minutes to prevent over-baking.
