To prepare dough, combine flours, salt, and 1 tablespoon sugar in a food processor or mixer bowl. Add butter and mix with a fork or pastry cutter until pieces of butter are uniformly pea-sized. Add water, one tablespoon at a time, until dough holds together when pinched, but is still crumbly. Place dough onto a lightly-floured surface and work it gently into a smooth ball. Wrap in plastic and refrigerate for 20 minutes.
Preheat oven to 375˚F. While dough is being refrigerated, prepare the apple filling. Slice halved apples into 1/8-inch-thick pieces. Gently toss apples with lemon juice, 2 tablespoons butter and sugar in a large mixing bowl. Set aside.
To prepare for filling, place chilled dough onto a floured piece of parchment paper, large enough to line a large rimmed sheet pan approximately 12 by 16 inches. Roll dough to form a rectangle, about 1/8 inch thick. Fold over excess dough over to form a decorative, free-form border. Transfer dough and parchment paper to a rimmed baking sheet and brush with remaining 1 tablespoon melted butter. Sprinkle edges with remaining 1 tablespoon sugar.
To fill, shingle sliced apples in a diagonal pattern, overlapping each by half an apple slice (side to side and top to bottom). Bake until crust is golden brown and apples begin to caramelize, about 40 minutes. Cool slightly and brush tops of apples with melted jelly. Drizzle with warmed caramel sauce and sliced almonds. Serve.
*Almond flour is available in most health food stores, many supermarkets, and is widely available online. To make almond flour, grind blanched slivered almonds in a food processor until finely ground; do not let it become a paste. Refrigerate until use.
Nutrition information per serving for 10 servings:
Calories 370, Cholesterol 40 mg, Total Fat 19 g, Fiber 2 g, Saturated Fat 10 g, Calcium 36 mg, Monounsaturated Fat 6 g, Magnesium 23 mg, Polyunsaturated Fat 1 g, Potassium 115 mg, Carbohydrate 50 g, Sodium 81 mg, Protein 4 g, Vitamin E 2.7 mg*
* Total Alpha-Tocopherol Equivalents