Pre-heat the oven to 350°F. Coat a 9x9 bakng dish lightly with butter or cooking spray.
In a medium saucepan, over medium-low heat, combine the peaches, cornstarch, water, brown sugar, and cinnamon. Bring the mixture to a boil, making sure to stir frequently. Add the butter, lemon, and vanilla extract and continue to boil the mixture for 2 more minutes to allow the filling to thicken.
Remove the saucepan from the heat and transfer the mixture into the 9X9 baking dish. Set aside
In a large bowl, combine the dry ingredients for the crust. In a separate bowl, combine the melted butter, non-dairy milk, and vanilla extract. Slowly pour the wet mixture into the dry ingredients and stir until just combined. (If the mixture is too dry, add 1 tsp of non-dairy milk at a time until the dough comes together).
In a small bowl, combine the coconut sugar, cinnamon, and nutmeg together for the cinnamon sugar topping. (you can skip this step if you'd like)
Spoon the dough on top of the peach mixture. It is okay if there are a few gaps. If you would like to even out the dough, coat your hands in a bit of olive oil and spread the dough as you'd like. Sprinkle the cinnamon sugar evenly on top of the dough
Bake for 35 minutes, or until the top is golden and the fruit is bubbling. Remove the cobbler from the oven and set aside to cool for at least 20 minutes before serving. Enjoy!