Preheat oven to 375 degrees F (190 degrees C). Grease a 10-inch springform pan and line with parchment paper.
Combine butter, 1 cup plus 2 tablespoons flour, 1/4 cup plus 2 tablespoons sugar, and 1 teaspoon vanilla extract in the bowl of a food processor; pulse until mixture resembles breadcrumbs. Turn out onto a clean work surface and quickly form into a ball. Dust a large piece of plastic wrap with flour and place pastry on top. Cover with a second piece of plastic wrap and roll out between the wrap to fit the 9-inch springform pan.
Place pastry into the bottom and the sides of the prepared springform and prick numerous times with a fork. Line pastry with parchment paper and a layer of pie weights or dried beans. Bake in the preheated oven until the pastry crust is firm but not hard, about 15 minutes. Let the pastry cool for 5 minutes. Carefully remove the parchment paper and weights; continue baking until the crust sets, about 5 minutes more.
Layer thinly sliced apples evenly over the pre-baked pastry crust.
Whisk creme fraiche, eggs, and vanilla extract together in a bowl. Pour over apples.
Bake tart in the preheated oven on top of a baking sheet (in case some filling spills) until tart is set and the top is golden brown, about 30 minutes. The filling should still be a little wobbly, as it firms up while cooling.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Strain apricot jam through a sieve. Combine apricot jam and water in a saucepan and heat until runny, about 3 minutes. Brush the jam over the top of the tart. Mix sugar and cinnamon in a small bowl and sprinkle over tart.
Place tart under the broiler until the top is golden brown, about 1 to 2 minutes.