Preheat the oven to 400°F (200°C).
Slice the peaches in half and remove the pits.
Arrange the peach halves cut-side up in a baking dish.
Place a thin slice of butter in the center of each peach half.
Sprinkle the peaches with cinnamon and a pinch of nutmeg.
Top each peach with a spoonful of brown sugar.
Bake for 15–20 minutes, or until the peaches are tender and the brown sugar has melted into a caramel-like sauce.