Preheat oven to 375°F (190°C). Lightly butter a 9×13-inch baking dish.

In a large bowl, combine the peaches, granulated sugar, brown sugar, cornstarch, lemon juice, vanilla, cinnamon, nutmeg, and salt. Toss until evenly coated.

Pour the peach mixture into the prepared baking dish.

In another bowl, whisk together the flour, sugar, baking powder, salt, and cinnamon.

Cut the cold butter into the flour mixture until it resembles coarse crumbs.

Stir in the milk and vanilla just until combined. Do not overmix.

Drop spoonfuls of the batter evenly over the peaches, leaving small gaps for the filling to bubble through.

Sprinkle with coarse sugar if desired.

Bake for 40–45 minutes, or until the topping is golden brown and the peach filling is bubbling around the edges.

Cool for 10–15 minutes before serving. Enjoy warm with vanilla ice cream.