In a mixing bowl, add oats, brown sugar, flour, and cinnamon. Use a pastry blender to mix in the butter until fully incorporated. Use a spoon to stir in coconut or nuts (if using).
In a large bowl, carefully mix together peaches, flour, and sugar.
Add peaches to baking dish and sprinkle evenly with oat topping.
Bake for 35 minutes, or until bubbling. After 30 minutes, place a loose sheet of foil on top if the topping is browned. It should be bubbling on the edges. Let cool for 5 minutes before serving (helps it thicken a bit).
Notes
To use frozen peaches, simply defrost the peaches and use them in place of the fresh peaches. Do not drain the peaches.
To bake in individual servings, divide peaches evenly between 6 greased one-cup-sized ramekins. Distribute the topping evenly over the ramekins. Place the baking dishes on a baking sheet or tray (lined with parchment in case of any spills). Bake 25-30 minutes.
Leftovers will keep in the refrigerator for up to 3 days, or in the freezer for up to 3 months. Thaw in the refrigerator and rewarm in the oven uncovered, or just recrisp the topping under the broiler for a minute.