In the bowl of a food processor, pulse the hazelnuts until they have the texture of coarse sand. Add the butter, sugar, flour, and salt, and pulse again until the mixture comes together and forms a dough.

Gather the dough into a ball, then press into the bottom and sides of a 10 or 11-inch tart pan with removable bottom. Transfer to the freezer and chill for at least 15 minutes.

Preheat oven to 350˚ and set a rack to the lower position. Rinse out the bowl of the food processor, then set it back on the base and add the cream cheese, sugar, cream, egg, vanilla, and salt. Process until evenly mixed, about 1 minute.

When the crust is chilled, set the tart pan on a baking sheet and pour the cheese mixture into the shell. Arrange the apple slices around the tart, pressing them lightly into the filling. Transfer to the oven and bake until the filling is set and the crust is lightly browned, about 35 minutes. Transfer to a wire rack to cool completely. Serve with Salted Caramel Sauce.

To make caramel sauce: Pour 3/4 cup water into a 3- to 4-quart saucepan and set over high heat. Add 1 cup granulated sugar in a mound in the center of the pot. Cover the pot and cook until the sugar dissolves and the mixture begins to bubble. Reduce heat to medium-low and continue simmering until the mixture turns a pale amber, 12 to 15 minutes. Do not swirl or stir during this time. Remove lid and watch the caramel closely. When it turns a darker amber color, remove it from the heat and carefully add 1 cup heavy cream—there will be a burst of steam, so be careful. Add 1/2 tsp. kosher salt and stir. Serve warm.