Heat oven to 325 degrees. Place apples in a small bowl, and toss with lemon juice; set aside. Butter six 8-ounce ramekins or custard cups; place in a roasting pan. Cut brioche into eight slices, then quarter each slice; set brioche aside.
In a large bowl, whisk together cream, eggs, sugar, salt, vanilla, and nutmeg. Add brioche, and toss to coat.
Place 1 tablespoon caramel sauce into each ramekin. Add approximately 1/3 cup apple mixture, then 1/3 cup bread mixture. Add a second layer of sauce, apple, and bread.
Carefully place the roasting pan on the center oven rack. Fill roasting pan with hot water to within 1/2 inch of ramekin tops. Cover pan with aluminum foil. Cook 20 minutes. Remove foil; cook 20 minutes more. Remove roasting pan from the oven, and transfer ramekins to a wire rack to cool 5 minutes. Using a towel, invert ramekins onto serving platter. Serve warm with remaining caramel sauce on the side.