For the filling: Preheat the oven to 350 degrees F. Add the peaches, maple syrup, arrowroot, vanilla and cinnamon to a large bowl, and mix thoroughly to combine. Transfer the fruit mixture to an 8-by-11-inch baking dish, and spread out in an even layer.
For the topping: Combine the almond milk and lemon juice in a small bowl, and set aside for 5 minutes to "clabber" (curdle). Sift the flour, baking powder, cinnamon and baking soda into a medium bowl; add the coconut sugar and salt, and whisk to combine. Drizzle the coconut oil into the flour mixture, and use your hands to work the oil in until all the flour is moistened. Add the clabbered almond milk and the maple syrup, and stir until just incorporated.
Crumble the topping over the filling, and bake until the fruit is bubbling and the topping is browning around the edges, 20 to 25 minutes. Remove the cobbler from the oven, and set aside for 10 minutes before serving.
Courtesy of Amy Chaplin