Preheat oven to 375°F (190°C).
In a 9x9-inch baking dish, combine sliced peaches, maple syrup, cinnamon, and vanilla extract until evenly coated.
In a medium mixing bowl, whisk together the whole wheat pastry flour, baking powder, and salt.
Incorporate the chilled butter into the flour mixture using a pastry cutter or fork until the texture resembles coarse crumbs.
Gently stir in the almond milk until a sticky dough forms, taking care not to overmix.
Drop rounded tablespoons of the dough onto the peach mixture, leaving small gaps between the portions.
Bake for 30 to 35 minutes until the peach filling is bubbling and the topping has turned golden brown.
Remove from oven and allow the cobbler to set for 10 minutes before serving.