Preheat the oven to 400°F. Grease a 13x9" baking dish or 10" skillet with butter.
In a large bowl, stir together the peaches, cornstarch and vanilla. Pour the peaches, including any juices, into the prepared baking dish.
In a separate large bowl, whisk together the flour, sugar, baking powder, baking soda and salt. Add the cubed butter, and using your fingers, work it into the flour mixture until the texture resembles wet sand.
Stir in the buttermilk and thyme, mixing just until combined.
Using two spoons, drop eight mounds of the cobbler dough atop the peaches, spacing them roughly 1 inch apart. Brush the tops of the biscuits with additional buttermilk and sprinkle with sanding sugar (optional).
Bake the cobbler until the filling is bubbling and the biscuits are golden brown and puffed, 30 to 35 minutes.
Remove the cobbler from the oven and let it cool slightly before serving.