In a 12-inch frying pan or 5- to 6-quart pan over high heat, melt 1½ cups butter. Stir often until the milk-solid particles turn golden brown, 5-7 minutes. Remove at once from heat; let stand until warm, 15 to 20 minutes (or nest pan in cold water and stir often, 5 to 8 minutes).
Meanwhile, in a food processor, whirl ¾ cup slivered almonds to a fine powder (or finely grate with a nut grater); scrape into a large bowl. Spread remaining 1 cup slivered almonds in a 10 by 15-inch pan.
Bake in a 350°F oven until almonds are golden brown, 6 to 12 minutes. Let cool slightly, then coarsely chop.
To the bowl containing ground almonds, add toasted almonds, sugar, and 1¼ cups flour. Stir to mix well.
Scrape melted butter with all browned particles into bowl; mix. Add egg whites, lemon peel, and orange peel. Beat with a mixer on medium speed, scraping bowl often, until batter is well blended. Add chopped apples and stir to mix.
Butter and flour a 9-inch cheesecake pan with removable rim. Scrape batter into pan.
Bake in a 325°F oven until cake is golden brown, firm in the center when lightly pressed, and begins to pull from pan sides, 1 hour to 1 hour and 10 minutes.
Let cake stand in pan on a rack at least 20 minutes or until cool, about 1 hour. Slide a thin-bladed knife between warm or cool cake and pan rim; remove rim. Set cake on a rimmed plate and, if desired, pour about ½ cup warm caramel sauce over the top. Cut into wedges; serve with scoops of ice cream and remaining caramel sauce to add to taste.
In a 3- to 4-quart pan over high heat, stir 3 Tablespoons salted Challenge European Style Butter and 2/3 cup sugar until mixture is caramel-colored, 2 to 4 minutes.
Remove from heat and add 2/3 cup whipping cream; stir until blended (mixture foams).
Return to high heat; stir until caramel sauce comes to a rolling boil, 1 to 2 minutes. Serve hot.