Preheat your oven to 350F. Grease a 9 x 13-inch dish and set it aside.
Mix your peaches, brown sugar, lemon juice, vanilla extract, and xanthan gum in a bowl until well combined. Pour this mixture into the greased dish, spreading it out evenly. Pop it into the oven and bake for 15 minutes.
While the filling is baking, prepare the biscuit topping. In another bowl, mix together the almond flour, arrowroot powder, baking soda, and salt. Stir in the melted coconut oil, maple syrup, and milk until you get a thick dough.
Take the dish out of the oven and drop spoonfuls of the biscuit dough on top of the peach mixture. Return it to the oven and bake for another 15-20 minutes, until the top is golden brown.
Let the peach cobbler sit for five minutes before serving.