How to Make It
Preheat the oven to 325°. Spray a 9-by-5-inch loaf pan with vegetable oil spray and line it with plastic wrap, allowing at least 3 inches of overhang all around. Spread the almonds in a pie plate and toast for about 7 minutes, until lightly golden. Transfer the almonds to a food processor and let cool. Add the almond paste, 2 tablespoons of the sugar and 1/4 teaspoon of salt and process until the nuts are finely chopped.
In a small saucepan, combine 1/4 cup plus 2 tablespoons of the sugar with 1/4 cup of water and bring to a boil. Boil over moderate heat until the syrup is slightly thickened but not colored, 4 to 5 minutes.
In a large bowl, using an electric mixer, beat the whole eggs with the egg yolk at medium-high speed until frothy. Slowly and carefully pour in the hot sugar and beat at high speed until fluffy and cool, about 7 minutes.
In another large bowl, beat the cream with the vanilla extract until firm. Fold the beaten egg mixture into the cream until no streaks remain. Fold in the almond mixture and scrape into the loaf pan. Cover with plastic wrap and freeze until solid, at least 6 hours or overnight.
In a large skillet, combine the remaining 1/2 cup of sugar with 2 tablespoons of water and the vanilla bean and bring to a boil. Boil over moderate heat, swirling the pan, until a deep, amber caramel forms, about 5 minutes. Add the apples and cook, stirring occasionally, until any liquid evaporates and the apples are tender, about 4 minutes. Add the cider and boil until a thick syrup forms, about 3 minutes longer; discard the vanilla bean.
Unmold and unwrap the semifreddo and cut into 8 slices. Spoon the caramelized apples on top and serve right away.