For the crust:
Combine flour, sugar, salt, and butter in a medium bowl. Using a pastry blender or your fingers, mix the butter into the dry ingredients until it is in pea-size pieces, about 5 minutes.
Add egg yolks and 4 tablespoons ice water and mix just until the dough comes together. (Add an additional 2 to 3 tablespoons ice water if necessary, but do not overwork the dough or it will become tough.) Shape into a flat disk, cover in plastic wrap, and refrigerate for at least 1 hour. Meanwhile, make the filling.
For the filling:
Combine the peels, cores and spices in a pan with the water and sugar.Heat over medium high fire until it melts, then cook it down a bit. Pour off 1 cup, and save the rest for another use.
Combine all the rest of ingredients in a large frying pan over medium heat. Add in 1 cup of the syrup. Cook, stirring, until the apple juices begin to release, about 4 minutes. Simmer until apples are tender on the outside but still firm when a knife is inserted in the middle, about 15 to 20 minutes more.
Remove from heat. Using a slotted spoon, transfer apples to a shallow dish to cool for at least 10 minutes. Set the pan with the reserved juices aside for later use.
To assemble:
Once the dough has chilled, place it on a lightly floured surface and, using a floured rolling pin, roll into a 16-inch circle (about 1/4 inch thick). Transfer to a parchment-lined baking sheet. Loosely fold in the edges of the pastry as needed to fit on the baking sheet, transfer to the refrigerator, and chill at least 30 minutes. Meanwhile, heat the oven to 425°F and arrange a rack in the middle.
Remove the dough from the refrigerator and unfold any edges. Spread the cooled apples in the center of the pastry, leaving a 2-inch border.
Fold the edges of the dough over the filling, covering about 1 inch of the apples and pleating the dough every 2 inches as you go.
Dot the apples with the butter, then brush the pastry edge lightly with water and sprinkle with the coarse sanding sugar. Bake the galette until the pastry is golden and the apples are tender, about 40 to 45 minutes.
While the galette is baking, return the frying pan with the apple juices to medium heat and reduce to 1/4 cup, about 20 minutes. Remove from heat, stir in the Calvados, and set aside.
Transfer the baked galette to a rack and pour the Calvados mixture over the apples. Serve warm with Vanilla Bean Ice Cream.
Beverage pairing: Badia di Morrona Vin Santo, Italy. Made from partially dried grapes, Vin Santo typically has wonderful toasted nut, apricot, and pear flavors with a little vanilla spice. These will complement the apples and cinnamon without stepping on them, while good acidity will lift the dessert.
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