In a large bowl, whisk together flour, sugar, and salt. Add the cold, cubed butter and use a pastry cutter or your fingertips to work it into the flour until the mixture resembles coarse crumbs with some pea-sized pieces remaining.
Drizzle in ice water, 1 tablespoon at a time, mixing gently with a fork until the dough just begins to come together. You might not need all the water – stop when the dough holds together when pinched.
Turn the dough onto a lightly floured surface and form into a disk without overworking. Wrap in plastic and refrigerate for at least 30 minutes or up to 2 days.
While the dough chills, preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
Peel, core, and slice the apples into thin, ⅛-inch slices.
In a large bowl, toss the apple slices with sugar, flour, cinnamon, nutmeg, lemon juice, and vanilla extract until evenly coated.
Remove the chilled dough from the refrigerator and let it sit for about 5 minutes to slightly soften. On a lightly floured surface, roll the dough into a 12-14 inch circle approximately ⅛-inch thick.
Transfer the dough to the prepared baking sheet.
Arrange the apple slices in an overlapping pattern on the dough, leaving a 2-inch border around the edges. Leave any accumulated juices in the bowl to prevent a soggy bottom.
Dot the arranged apples with small pieces of cold butter.
Gently fold the edges of the dough over the apples, pleating as needed. The center of the filling will remain exposed.
Brush the folded dough with egg wash and sprinkle with coarse sugar.
Bake for 40-45 minutes until the crust is golden brown and the filling is bubbly. If the edges brown too quickly, loosely cover them with foil.
Let the galette cool for at least 15 minutes before slicing. For an extra touch of elegance, brush the exposed apple filling with warmed apricot jam while still warm.