Prep the peaches. If using fresh peaches, peel if you like (the skins soften, so peeling is optional).
Slice into 1/2-inch wedges. If using frozen, no need to thaw completely—just break up any large clumps.
Heat the oven. Set to 375°F (190°C). Butter a 9x13-inch baking dish or a deep 10-inch skillet.
Make the peach filling. In a large bowl, toss 6 cups peaches with 1/2 cup granulated sugar, 1 tablespoon lemon juice, 1 teaspoon vanilla, 1 1/2 tablespoons cornstarch, 1/2 teaspoon cinnamon, and a pinch of salt.
If your peaches are very tart, add 2 more tablespoons sugar.
Pre-bake the fruit. Spread the peaches in the dish. Dot with 2 tablespoons butter. Bake for 10–12 minutes until the fruit starts to release juices and bubble at the edges.
This prevents a watery cobbler.
Mix the dry ingredients. In a medium bowl, whisk 1 1/2 cups all-purpose flour, 2 teaspoons baking powder, 1/4 teaspoon baking soda (if using buttermilk), 1/2 teaspoon salt, and 1/2 teaspoon cinnamon. For extra warmth, add a pinch of nutmeg.
Cut in the butter. Add 6 tablespoons cold unsalted butter, cut into small cubes. Work it into the flour with a pastry cutter or your fingertips until it looks like coarse crumbs with some pea-sized pieces.
Add the sourdough and liquid. In a measuring cup, stir 3/4 cup sourdough starter with 1/3 cup milk or buttermilk and 2 tablespoons granulated sugar (or brown sugar for a deeper flavor).
Pour into the flour mixture and gently fold until it just comes together. The dough should be soft and slightly sticky. If it’s dry, add 1–2 teaspoons more milk.
Top the peaches. Remove the hot dish from the oven.
Drop spoonfuls of dough over the fruit, leaving small gaps for steam to escape. For a smoother top, lightly pat the mounds with damp fingers. Brush with a little cream and sprinkle with coarse sugar if you like.
Bake until golden. Return to the oven and bake 25–35 minutes, until the topping is golden brown and the peach juices are thick and bubbling in the gaps.
A toothpick in the thickest biscuit should come out clean.
Rest before serving. Let it cool 15–20 minutes so the juices thicken. Serve warm with vanilla ice cream, lightly sweetened whipped cream, or a drizzle of cold heavy cream.