Whisk the sugar, salt, and 3 cups flour together in a medium bowl. Using a pastry cutter, a food processor, or using your fingers, cut in the extremely cold butter (I leave mine in the freezer for 10 minutes before using) until the mixture resembles coarse, pea-sized crumbs. Add the water and mix gently until the flour is moistened.

Gently knead the dough a few times on a lightly floured work surface until it all comes together. Shape the dough into 2 separate dough balls and flatten them into thick disks. Wrap each disk separately in plastic wrap and refrigerate for at least 1 hour.

As the dough rests, mix the apples, brown sugar, flour, lemon juice, cinnamon, and nutmeg together in a large bowl. Cover bowl with plastic wrap and let sit in the fridge until the dough is ready.

Preheat oven to 425 degrees F (220 degrees C). Line a large baking sheet with parchment paper or a silicone baking mat. Set aside.

On a lightly floured work surface, roll one of the dough disks into a 12-inch shape (round is a shape. Oval is good. Rectangle works, too.) Transfer dough to the prepared baking sheet.

Arrange the apples onto the center of the dough in one single layer. They can overlap, but do not pile them on like an apple pie. Leave a 1-2 inch border around the pastry. Fold the edges of the dough over the apples, overlapping the dough where needed. Remember, this is rustic, so be as imperfect as you want. Press gently to seal the edges, then brush the crust with the egg wash and sprinkle the raw sugar over the crust.

Bake until the filling is bubbly and the crust is golden brown, about 33-35 minutes. Allow to cool on the baking sheet for 10 minutes before slicing and serving.

Repeat baking instructions with the second dough disk and the rest of the apples to create a second galette.

Serve with a hearty drizzle of caramel sauce on top.

In a 3-quart stainless steel saucepan with a candy thermometer attached, combine water, sugar, and salt over medium heat. Stir with a fork until the syrup comes to a boil, then simmer without stirring until syrup is honey-colored, roughly 7-10 minutes, shaking and swirling the pan as needed. Remember, no stirring! Continue cooking until syrup is a medium amber color, not too dark. Immediately add cream (this will make the caramel act up, bubbling and spitting so be careful) and reduce heat to medium-low.

Stirring constantly with a heat-resistant spatula, simmer until caramel is 225 degrees F (107 degrees C) on a candy or digital thermometer, it'll take about 3 minutes. Transfer to a heat-resistant container, stir in vanilla extract, and cool to room temperature. Caramel will be runny while warm, but will thicken as it cools. Rewarm with a touch of cream over low heat in a saucepan if needed when cold.