To begin, preheat your oven to 190°C (170°C fan). In a medium mixing bowl, combine sliced peaches with both sugars, lemon juice, cinnamon, nutmeg, flour, and a pinch of salt. Gently stir to coat the fruit evenly and allow to sit for 10 minutes while you prepare the topping.
In a separate large bowl, whisk together the flour, baking powder, salt, and sugar. Add the cold butter pieces and rub them into the flour using your fingertips until the mixture resembles coarse breadcrumbs. This helps create a flaky texture in the topping.
Pour in the milk and vanilla extract. Stir just until the dough comes together into a sticky batter. Avoid overmixing to keep the topping light and tender.
Transfer the macerated peaches with their juices into a buttered 20cm square baking dish. Spread them evenly across the bottom.
Drop spoonfuls of the dough over the peaches, leaving some gaps to allow the filling to bubble through. Do not flatten the dough; let it spread naturally while baking.
For extra texture and sparkle, sprinkle demerara sugar evenly over the dough topping.
Place the dish on the centre rack and bake for 35 to 40 minutes or until the topping is golden and a skewer inserted into the dough comes out clean. The filling should be bubbling at the edges.
Remove the cobbler from the oven and allow it to rest for at least 10 minutes before serving. This helps the filling settle and intensifies the flavours.
Serve warm, ideally with a scoop of vanilla ice cream or a dollop of fresh whipped cream. The cold creaminess pairs beautifully with the warm, spiced fruit.
For a homely yet elegant presentation, serve the cobbler straight from the baking dish at the table. Leftovers can be covered and stored in the fridge for up to 3 days. Reheat gently in the oven to maintain the texture.