To prepare the crust: To prepare the crust, place the flour, 7 tablespoons butter, sugar and salt in the food processor and process just until mixture has the texture of coarse crumbs, 10-12 seconds. Add the ice water and pulse about 6-8 times. Don’t let the mixture form a ball; stop when it just begins to hold together. Transfer the pastry to waxed paper and flatten the dough into a disk. Add 1 tablespoon of flour at a time if the dough seems too sticky. Wrap in the waxed paper and refrigerate for at least an hour.

When the crust has chilled, roll it out thinly into a 10-11 inch disk on a lightly-floured surface. Place it on a 9-inch round tart pan with a removable bottom. Carefully press the pastry into the pan and up the side. Tuck the overhang inside the pan leaving, pressingly slightly to create a sturdy shell. This will also compensate for any shrinkage to the dough during baking. Prick the bottom and sides of the shell with a fork and chill for another 20 minutes before baking.

Preheat your oven to 375°F. Cover the pastry with aluminum foil and fill with pie weights or rice/beans. Bake the shell until it just starts to brown, about 15-20 minutes. Remove from oven and allow to cool while you prepare the filling.

To prepare the apples: Toss the sliced apples in a bowl with the lemon juice to prevent discoloration. In a large skillet, melt the butter over medium-high heat and add the apples and the sugar. Sauté the apples, shaking the pan occasionally, until they're slightly brown, about 15 minutes.

To prepare the custard: While the apples cook, beat the eggs and sugar in a large bowl with an electric mixer until thick and pale. Add the melted butter and vanilla and continue to mix on high speed until the ingredients are thoroughly incorporated.

Assembly: Arrange the apples along the bottom of the partially-baked tart shell then pour the custard mixture over the apples. Sprinkle the chocolate chips over the apples and bake until golden, about 30 minutes.

Cool before serving.