Preheat your oven to 375°F (190°C).

Combine 4 cups of sliced peaches, 1/2 cup of granulated sugar, and 1/2 cup of brown sugar in a medium saucepan and let sit for 5 minutes.

Cook the mixture over medium heat until boiling, then reduce to a simmer for about 10 minutes.

In a baking dish, melt 1/2 cup (1 stick) of unsalted butter in the oven.

In a separate bowl, whisk together 1 cup of flour, 1 tablespoon of baking powder, 1/4 teaspoon of salt and 1/2 cup of granulated sugar. Gradually stir in 1 cup of milk and 1/2 teaspoon of vanilla extract.

Carefully pour the batter over the melted butter in the baking dish. Spoon the peach mixture evenly over the batter without stirring.

Sprinkle 1/2 teaspoon of ground cinnamon and optional 1/4 teaspoon of ground nutmeg on top.

Bake the cobbler for about 40-45 minutes, until the top is golden brown and bubbly.

Let the cobbler cool for about 10 minutes before serving.

Serve warm, optionally with ice cream or whipped cream.