Preheat the oven to 375°F and generously butter a medium sized baking dish (we used an 11 x 7 oval, but a 9 x 9 or a 10 inch skillet would also be great!).
Pit and thinly slice the peaches into half-moon shapes about ¼ inch thick. Place the peaches in your prepared dish and top with brown sugar, flour and vanilla extract. Use your hands or a wooden spoon to toss to combine. Once the peaches are evenly coated, gently spread them back into an even layer. Set aside.
Next, make the cobbler. In a large mixing bowl combine the flour, sugar, baking powder and salt. Use a pastry cutter to cut the butter into the dry ingredients until the mixture starts to clump up. It’s okay to still have big chunks of butter throuhout.
Make a well in the center of the dry ingredients and add the buttermilk and vanilla extract. Stir everything together until it forms a wet biscuit dough. It will be sticky at first, but it will thicken as it sits.Use two large spoons to drop the biscuit dough into big clumps over the peaches. Sprinkle sugar over the topping. This will give your topping a golden crunchy finish.
Place in the oven to bake for 40 to 50 minutes or until the peaches are bubbling and the topping is golden brown all over.
Allow to cool for 10 minutes before serving hot with vanilla ice cream or whipped cream.