Prepare a bowl of ice water. Blanch the peaches. Bring a large pot of water to a boil. Drop the peaches in the boiling water for 15-20 seconds, then remove and plunge immediately into the cold water. Drain the peaches and peel them-- skin should slip right off.
Preheat oven to 400F.
Cut the peaches in half along the "line" that divides the fruit and remove the stone. Put the peaches cut side up in a shallow baking pan so that they all fit in one layer. In a small bowl, mix together the brown sugar and nutmeg, then cut in the butter using your fingertips. Sprinkle over the peaches. Bake for 20-25 mins.