PATE SUCREE: Pulse flour, sugar and salt in a food processor to combine. Add butter, and process until mixture resembles coarse meal, about 10 seconds.
Lightly beat egg yolks with water in a small bowl. With machine running, add yolk mixture to the flour mixture, and process until dough just holds together (no longer than 20 second). Divide dough into 2 disks, and wrap in plastic, and refrigerate for 2 hours (or up to 2 days).
Divide both disks of pâte into 3 portions. On a lightly floured work surface, roll each disk into a 1/8-inch-thick round. Combine sugar and cinnamon. Sprinkle 1 teaspoons of the mixture over each of dough rounds.
Combine 2 tablespoons cinnamon-sugar mixture, the jam, walnuts, brown sugar and lemon juice in a small bowl.
Peel and core apples, creating a cavity about 1-inch wide. Place each apple in the center of a dough round, spoon 1 1/2 tablespoons jam mixture into each apple. Starting on one side, press dough against apple. Gather the dough at the top and trim any excess, leaving just enough to pinch closed. Place apples on a parchment lined baking sheet.
Refrigerate until firm, 45-60 minutes.
Preheat oven to 350°F.
Lightly beat egg with water. Brush apples with egg wash. Sprinkle with cinnamon-sugar mixture to taste. Bake until golden brown, 45-55 minutes.
Serve warm or at room temperature, with whipped cream.