Preheat your oven to 375°F (190°C) and lightly grease a 9×9 inch baking dish.

In a large bowl, combine the sliced peaches, granulated sugar, cornstarch, vanilla extract, ground cinnamon, ground nutmeg, lemon zest, and lemon juice. Toss everything together until the peaches are evenly coated.

Transfer the peach mixture into the prepared baking dish, spreading it out into an even layer.

In another bowl, whisk together the all-purpose flour, granulated sugar, baking powder, and salt.

In a separate small bowl, mix together the non-dairy milk, melted vegan butter, and vanilla extract.

Pour the wet ingredients into the dry ingredients and stir until just combined. Be careful not to overmix!

Drop spoonfuls of the cobbler batter over the top of the peaches in the baking dish, covering them as evenly as possible.

Place the cobbler in the preheated oven and bake for 35-40 minutes, or until the filling is bubbly and the cobbler topping is golden brown.

Once done, remove the cobbler from the oven and allow it to cool for a few minutes before serving.

Serve warm, optionally topped with a scoop of vegan vanilla ice cream or dairy-free whipped cream.