In a food processor, combine the flour with the sugar, salt and butter and process for about 5 seconds.
In a small bowl, whisk together iced water and vinegar.
With the machine running, pour the water vinegar mixture down the feed tube and pulse until the dough begins to form. You should still be able to see small pieces of butter in it.
Transfer the dough to a floured surface and form the dough into a disk. Wrap the dough in plastic wrap and refrigerate for 1 hour.
With a non-stick pan over medium-low heat, place the hazelnuts in the pan and move them around until they become fragrant and slightly golden brown. Keep a close eye on them as they burn easily.
Let them cool, then rub the hazelnuts with a clean and dry dish towel, removing as much of the skin as possible.
In a food processor, pulse the hazelnuts until finely ground.
Add flour, butter, sugar, egg, vanilla, and rum and process until creamy. Transfer the hazelnut to a tight lidded container and refrigerate until until ready to use.
Peel, halve and core the apples and slice them crosswise 1/8 inch thick.
Combine sliced apples, sugar, lemon juice, and cornstarch, in a large bowl. Gently fold to coat apples.
On a lightly floured work surface, roll out the pastry to a 10-by-14-inch rectangle and transfer to a large rimmed baking sheet.
Spread about ¾ cup of frangipane over the rolled out dough, leaving the edges free from filling, about 1 1/2" border.
Arrange apple slices on top of dough, leaving a 1 1/2" border around the edge.
Fold the edge nearest to you towards the center. Rotate sheet plan slightly and repeat, until all edges are folded over the apples to create a 1-inch border.
Transfer the galette to the freezer for 15 minutes while you preheat the oven to 375°F.
Whisk together the egg with a pinch of salt in a small bowl. Brush the edges of the tart with the egg wash, then sprinkle with turbinado sugar all over the tart.
Bake the galette for about 55-60 minutes until the pastry is nicely golden brown and crisp and all of the apples are tender.
Transfer the pan to a rack and let the galette cool. Serve warm or at room temperature.