Sprinkle the yeast over the warm water in a small bowl. Let stand for a few minutes so the yeast can dissolve. In a separate bowl, combine sugar, shortening, caraway, salt, and nutmeg. Heat the milk in a small saucepan just until a skin forms on the top. Remove from the heat and stir into the shortening mixture. Allow to cool to lukewarm so that it will not kill the yeast.
Stir the egg and yeast into the bowl with the milk and gradually mix in the flour using a sturdy wooden spoon until the you get a stiff batter. Cover loosely and set aside in a warm place to rise until doubled in size, about 45 minutes.
Grease the cups of a muffin tin, and spoon batter into the cups filling half way full. Let rise again in a warm place until the dough rises above the top of the cups, about 1 hour.
Preheat the oven to 400 degrees F (200 degrees C).
Bake the rolls in the preheated oven until golden brown on top, 12 to 15 minutes.