Prep the oven and pan: Heat your oven to 375°F (190°C). Grease a 9x9-inch baking dish or similar 2-quart dish.
Combine the peaches: In a large bowl, mix peaches with sugar, cornstarch, vanilla, cinnamon, nutmeg, lemon juice, and a pinch of salt.
Stir until the peaches look glossy and evenly coated.
Make the peach layer: Spread the peach mixture evenly into the prepared baking dish. If using very juicy peaches, spoon off a little extra liquid so the cobbler doesn’t get soupy.
Mix dry topping ingredients: In a separate bowl, whisk flour, granulated sugar, brown sugar, baking powder, baking soda, and salt.
Cut in the butter: Add cold butter cubes and work them into the flour with a pastry cutter or your fingers until the mixture looks like coarse crumbs with pea-sized bits of butter.
Add liquids: Stir in buttermilk and vanilla just until the dough comes together. It should be thick and slightly sticky.
Avoid overmixing.
Top the peaches: Dollop spoonfuls of the dough evenly over the peach layer. It won’t cover completely; gaps are fine and help steam escape.
Finish and bake: Sprinkle the top with coarse sugar and a light dusting of cinnamon if you like. Bake 35–45 minutes, until the topping is golden and the peach filling is bubbling around the edges.
Rest, then serve: Let the cobbler cool for 10–15 minutes to thicken slightly.
Serve warm, ideally with vanilla ice cream or whipped cream.