In a large bowl, combine the sliced peaches and 1/3 cup of brown sugar. Set aside.
In another large bowl, mix together the flour, granulated sugar, salt, melted butter, vanilla, and baking powder until a dough forms.
Preheat your oven to 350°F. Evenly distribute the peach mixture inside a greased 9x13-inch pan.
Place small scoops of the dough all over the top of the peaches to cover them. Sprinkle the top generously with ground cinnamon.
Bake in the preheated oven for about 40-45 minutes, or until the top is golden brown and the peaches are bubbly. If desired, finish baking the cobbler under the broiler to brown it more. Serve warm.