Preheat the oven to 425 degrees F.
Generously butter a 1 1/2-quart shallow baking dish. Place the sliced peaches in the dish and sprinkle with brown sugar, cinnamon, vanilla, and flour. Mix gently and spread evenly again. Bake for 10 minutes.
Meanwhile combine all dry ingredients for cobbler crust in a bowl. Cut in the butter with a pastry cutter or your fingers, to make the texture like coarse crumbs. Add buttermilk and stir to form a soft dough.
Remove fruit from oven and drop rounded spoonfuls of dough on top. Sprinkle with last tablespoon of brown sugar and return to oven. Bake until fruit is bubbly and crust topping is golden brown, about 20 minutes. Serve warm with whipped cream.
Recipe courtesy of Kristina Williamson, Schooner Ellida, Rockland, Maine