Combine peaches, butter, sugar and nutmeg in a saucepan. Bring to a boil. Reduce heat. Simmer until peaches are tender and mixture starts to thicken, about 20 minutes. Pour into baking dish.
Combine flour, shortening, and salt, and mix with a pastry cutter. Add just enough cold water to make a crust, and roll out to fit the cobbler.
Lay the crust over the peaches and make several slashes with a sharp knife.
Bake 35-45 minutes, or until the crust just looks done.