Begin by preparing the tart crust. In a food processor, mix the flour, salt, and sugar, pulsing briefly until combined. Incorporate the cold butter cubes and process until the mixture resembles coarse crumbs. Then, add the egg yolk.

Add the ice water gradually, one tablespoon at a time, pulsing after each addition until the dough holds together in a ball form. Adjust the water if necessary.

Knead the dough gently until it forms a cohesive ball. Wrap it in plastic or place it in a covered bowl to chill in the refrigerator for about 30 minutes.

While the dough chills, prepare the apples. Slice them and place into a mixing bowl. Toss gently with lemon juice, cinnamon, brown sugar, and vanilla. Allow the mixture to rest for 15-20 minutes to soften.

Preheat your oven to 350°F. Grease a tart pan with butter. Roll out the dough on a floured surface to about 10-11 inches wide, then gently place it into the pan, trimming any excess dough.

Layer the apple slices on the crust in your preferred arrangement. Sprinkle a dash of sugar over the top and dot the surface with small bits of butter. Bake for approximately 60 minutes until the tart is golden brown, then let it cool.

To make the caramel, heat the sugar in a saucepan over medium heat, stirring frequently until it caramelizes to an amber hue. Carefully stir in the butter until melted, followed by the cream and salt, mixing until it thickens. Allow the caramel to cool in a bowl.

When serving, cut the tart into slices and drizzle with the warm caramel. Optionally, top with a sprinkle of sea salt and a scoop of vanilla ice cream for a delicious treat!