In a large bowl, whisk together the oats, sugar, baking powder, salt and nutmeg. In a small bowl, whisk together the milk, eggs, peach jam and vanilla extract. Add the wet ingredients to the dry ingredients stirring until everything is combined and wet. Scrape the mixture into the buttered dish and stir until most of the butter is incorporated, but leave some pockets of butter in the corners. Smooth out of the top and add the peach slices.