Preheat oven to 350 degrees F (175 degrees C). Butter a 2 quart baking dish.
In a 2 quart saucepan over medium heat, scald the milk and remove from heat. Add the rice, sugar and salt. Mix well and slowly add the eggs, vanilla, and butter. Pour mixture into a 2 quart baking dish. Sprinkle nutmeg on top. Bake for 40 minutes. Stir pudding after 20 minutes.