Combine fl our, sugar, and salt in a mixing bowl. Add the butter, working it in with a mixer or by hand until the pieces are the size of tiny peas. Add ice water, 1 tablespoon at a time, tossing and mixing gently by hand until the dough is moist but not sticky. Wrap the dough in plastic wrap and flatten into a disk. Refrigerate for at least 1 hour but preferably overnight.

On a floured surface, roll out the dough to a 12-inch circle. Don’t worry if it’s not perfectly round. Transfer the dough to a parchment-lined pizza pan or baking sheet. Cover with plastic wrap and refrigerate briefly.

Preheat oven to 400 degrees.

Remove the dough from refrigerator. Arrange the apple slices on the dough in neat concentric circles, just barely overlapping, leaving a 1- to 1½-inch border of pastry. Fold the pastry edges up over the apples to hold filling, making sure there are no cracks where the juices will leak out during baking. Brush apples and pastry with the melted butter and sprinkle with sugar. Bake until the dough is nicely browned at the edges and the apples are just beginning to brown, 30 to 40 minutes, rotating as needed so the tart browns evenly. Transfer to a cooling rack.

Pour cream into a medium saucepan and heat barely to a simmer. Set aside. Combine sugar and 1/3 cup of water in a heavy-bottom medium saucepan over medium heat. Leave undisturbed until the sugar begins to melt and darken. Gently shake the pan to distribute the sugar and to keep the melted sugar from burning. When all has melted and the caramel is a dark amber, remove from heat. Carefully and slowly add the hot cream and pinch of salt, stirring constantly with a wooden spoon. Return the pan to heat and keep the sauce at a gentle boil for about 3 minutes, stirring constantly. Serve warm. Will keep, tightly covered, in the refrigerator for 3 weeks.