Make the crust: In the bowl of a stand mixer fitted with the paddle attachment, combine flour, sugar, vanilla, egg, cold butter, and salt. Mix until the dough is smooth. It will look like crumbs at first but will come together after 1-2 minutes. Give it a quick knead by hand, press it into a disc, cover it with plastic wrap, and refrigerate for 30 minutes while making the filling.
2 ½ cups all-purpose flour, ½ cup granulated sugar, 1 teaspoon vanilla extract, 1 large egg, ¾ cup unsalted butter, ½ teaspoon salt
Preheat and prep pan: Preheat the oven to 350°F (175°C) and grease a 9-inch springform pan (26 cm) with soft butter, then dust with flour and tap out the excess.
Prepare filling: Peel and core the apples, then cut them into 1/2-inch chunks. In a bowl, combine apples, sugar, lemon juice, cinnamon, and rum (optional) until everything is evenly coated.
5 apples, ¼ cup granulated sugar, 2 tablespoons lemon juice, 1 teaspoon cinnamon, 2 tablespoons rum
Bottom and sides of the crust: Use 3/4 of the dough for the bottom. Roll out the dough into a circle about 2 inches bigger than your baking pan, transfer it to your pan, and bring up the dough on the sides. Pierce the bottom with a fork and sprinkle breadcrumbs on top.
2 tablespoons breadcrumbs
Filling and top crust: Transfer the apple filling into the crust. Roll out the remaining dough and use it to make the upper crust. Cover the filling with the crust and seal the edges. Pierce the top with a fork.
Baking: Bake for 45-50 minutes in the middle of the oven until the crust is lightly browned and the filling is soft. Let the cake cool in the pan. Then serve with homemade whipped cream.