Preheat oven to 375 degrees F. Grease an 8x8 baking dish with coconut oil.
Make the peach filling. In a medium-sized saucepan, combine the peaches, coconut sugar, arrowroot, lemon juice, and cinnamon. Cook over medium heat for 5-7 minutes. Then, transfer to the greased baking dish.
Make the cobbler topping. Combine almond flour, arrowroot, baking powder, coconut sugar, and a pinch of sea salt.
Add the solid chunks of coconut oil to the flour mixture until it becomes crumbly. Then, stir in the coconut milk and vanilla extract until a dough forms.
Scoop up the dough in small handfuls, flatten with your hands, and lay it all over the peach filling.
Bake for 30-40 minutes, or until the top is golden brown. Allow to cool for at least 10 minutes prior to serving.