Preheat the oven to 374º F (190° C). Line a large baking sheet with parchment paper. Separately, cut the peaches in half vertically, turning the knife from the top of the peach. Then, separate the halves and remove the pits.
In a small bowl, mix the melted butter with the brown sugar, cinnamon and nutmeg with a fork.
Place the cut peaches side up on the baking sheet and brush them with the butter mixture using a pastry or kitchen brush. Flip the peaches, now they should be skin up, and brush them with the same mixture until you use all of it.
Bake the peaches for 10 minutes. After this time, take them out of the oven, carefully flip them over once more and spread some of the butter mixture on the bottom of the baking sheet on top of them. Bake for another 15 minutes, until the peaches are soft and caramelized.
Remove the peaches from the oven and serve warm with ice cream or whipped cream as well as granola or nuts.