Preheat your oven to 400°F (200°C) and grease a 9x13-inch baking dish with butter.

In a medium saucepan, whisk together brown sugar, granulated sugar, and nutmeg. Add unsalted butter and water, stirring until the mixture boils gently. Remove from heat and let cool.

In a large mixing bowl, combine all-purpose flour, sugar, baking powder, salt, cinnamon, and nutmeg. Whisk to blend well.

Gradually stir in whole milk and vanilla extract, mixing until smooth. Fold in diced peaches evenly.

Pour the peach filling into the baking dish and drizzle the topping mixture over the filling without stirring.

Bake for 50 to 55 minutes until set and golden brown. If browning too quickly, cover loosely with foil.

Let cool for 15 minutes before serving warm, optionally with ice cream, whipped cream, or Cool Whip.