In a saucepan combine the cranberries, 1 cup of the sugar, and the nutmeg, cook the mixture over moderately high heat, stirring, until the sugar is dissolved, and boil it, covered, for 3 minutes. Simmer the mixture, uncovered, stirring, for 3 minutes and let it cool.
Into a bowl sift together the flour, the baking powder, the remaining 1/4 cup sugar, and salt. In another bowl whisk together the egg, butter and milk, add the mixture to the flour mixture, and stir the batter until it is just combined. Divide the cranberry mixture among 12 well-buttered 1/2-cup muffin tins, top it with the batter, and bake the muffins in the middle of a preheated 400 degree F oven for 25 minutes, or until they are golden. Let the muffins cool in the tins for 2 minutes and invert them onto a rack.