Place the butter in a large skillet and melt over medium heat. Swirl the pan to coat. Combine the apples, cinnamon, cloves, nutmeg, lemon juice and brown sugar in a large bowl and then add it to the skillet with the melted butter. Cook, stirring frequently, until apples are just turning soft, about 8-10 minutes.
Pour the apples into a buttered 11×7-inch baking dish.
Place the coconut flour, arrowroot flour, tapioca flour, cinnamon, 1/2 cup sugar, and baking powder into the bowl of a food processor and pulse to combine. Add the butter and pulse 15-20 times, until it is the size of peas. Add the beaten eggs and vanilla and pulse until the mixture is evenly moistened. Spoon dollops of the dough onto the peaches and sprinkle with the remaining 1 tablespoon of sugar.
Bake for 45-50 minutes, until the topping is just turning golden brown. Cool for 20 minutes and then serve.
For the Caramel: Melt the butter in a medium saucepan over medium heat. Whisk in maple syrup and bring to a boil. Whisk constantly for about 2 minutes. Slowly pour in cream. Bring to a boil, whisking often. Boil until sauce thickens and coats the back of a spoon, (or reaches 220ºF) about 5 minutes. Remove from heat and whisk in salt. Let cool for 10 minutes.
Serve the cobbler with caramel drizzled on top.
