Preheat oven to 350 degrees F. In a large bowl, combine the diced peaches, ¼ tsp cinnamon, ¼ tsp nutmeg, 1 tsp vanilla, and 2 Tbs lemon juice. Mix with a spoon. Add 2 Tbs tapioca flour and mix until distributed. Then, add the maple syrup to the bowl and mix again; set aside.
In another bowl, combine 1 cup almond milk, 1/2 cup coconut sugar, 3/4 cup almond flour, 1/4 cup tapioca flour, 2 Tbs coconut flour, 1 tsp baking soda, 1/2 tsp cream of tartar, a pinch of salt, 1/4 cup olive oil, 1 tsp cinnamon and 1/2 tsp nutmeg. Mix until smooth.
Grease an 8 x 8 inch pan. Pour the peaches into the pan. Then, pour the cobbler batter over the peaches, making sure to evenly distribute it on top of all the peaches.
Bake for 40-45 minutes, until the top has hardened and is cake-like. ( 40 minutes was plenty of time for me).
Note- you can use maple sugar or brown sugar instead of coconut sugar if you would like. Though brown sugar is not Paleo.