Peel, core, and cut apples into large dice. Melt 1/4 cup butter in a large, heavy skillet. Add apples, sprinkling with 2 tablespoons sugar and the cinnamon. Saute over medium heat for about 10 minutes, stirring frequently.
Remove crusts from bread and cut into 1/2 to 3/4-inch cubes. Liberally grease a deep, 2 1/2 quart, baking dish with the remaining 1/4 cup butter, then add what is left to the bread cubes, cutting into bits. Combine bread, raising, apples, and the pan juices into the baking dish.
Combine eggs, milk, sugar, vanilla, and nutmeg, beating lightly with a whisk. Pour over bread and apples.
Set dish in a shallow pan filled with 1-inch warm water. Bake for 1 1/2 hours until set. (This may take 2 hours, depending on type of casserole dish.) Serve hot with lightly whipped cream.