Cook 2-1/2 cups sugar in large heavy skillet over low heat until dissolved, without stirring, swirling pan occasionally. Add 4 lb apples and cook until tender and lightly carmelized, about an hour. Cool. Scald milk. In a bowl, whisk together eggs, 2/3 cup sugar and Calvados. Whisk mixture into milk. Place brioche in a flat pan just large enough to hold it and pour milk/egg mixture over it. Let set long enough so the brioche absorbs it all. Melt 1 cup butter in a large skillet over medium high heat. Add brioche in batches and brown well on both sides. Butter an 8" springform pan. Using 3/4 of brioche, line bottom and sides of pan. Spoon cooked apples atop brioche. Cover apples with remaining brioche. Top with a plate and weight with a small can of something-or-other from your cupboard. Refrigerate at least 3 hours, or overnight. When almost ready to serve, cook the last 1 cup sugar in a heavy skillet over low heat until dissolved, swirling pan occasionally. Increase heat to medium, add apples and cook until lightly carmelized, about 25 minutes. To serve, remove sides of springform pan. Top with hot apples and garnish with either rich vanilla ice cream or lightly sweetened whipped cream. ----