Preheat the oven to 335°F.
In a small saucepan over medium heat, add the peaches, coconut sugar, and 1/2 cup warm water. Bring to a simmer and cook for 7 to 10 minutes, until the peaches are cooked through and starting to soften. The timing will vary depending on whether you use fresh or frozen peaches.
In a glass or mug, thoroughly mix the remaining 2 tablespoons of water with the cornstarch until no small chunks of cornstarch remain. Press the slurry against the side of the glass to work out any lumps. The mixture should be thick and even. Add up to 1 more tablespoon of water if you need it.
Pour the cornstarch slurry into the saucepan with the peaches and stir to combine. Simmer for 1 minute. Take off the heat and stir in the lemon juice and butter.
Pour the peach mixture into a 9x9 glass baking dish and set aside.
In a medium bowl, combine the oat flour, coconut flour, Lakanto, baking powder, and salt. In a small bowl, combine the milk and melted butter.
Pour the milk and butter into the flour mixture. Stir just enough to combine.
Using a spoon, evenly distribute dollops of the batter over the peaches in the baking dish. Press the dollops down with the back of the spoon or a spatula so the peaches end up evenly covered by the batter.
In a small bowl, combine the coconut sugar and nutmeg. Sprinkle this mixture over the batter.
Bake for 25 to 30 minutes, until the batter is firm and golden.