In a food processor, blend together the all-purpose flour, granulated sugar, and salt until well combined. Add cold, cubed unsalted butter and pulse until the mixture resembles coarse crumbs. Gradually add ice water, processing until the dough clumps together. Shape it into a disk, wrap it in plastic, and chill in the refrigerator for at least 2 hours to ensure a flaky crust.

Preheat your oven to 400°F (200°C). Peel, core, and slice your baking apples into evenly-thin pieces. Toss the apple slices in a mixing bowl with lemon juice, sugar, and a sprinkle of cinnamon.

Once the dough is chilled, lightly flour your work surface. Roll the dough into a rough 12-inch circle. Transfer the rolled dough to a parchment-lined baking sheet.

Spread the prepared apple filling in the center of the dough, leaving a 3-inch border. Gently fold the edges over the apple filling, tucking and pleating as you go. Drizzle with melted butter.

Brush the exposed dough with beaten egg and sprinkle coarse sugar over the surface. Bake for 45 minutes, until the crust is golden and the filling is bubbly.

Allow the galette to cool on the baking sheet for at least 30 minutes before serving. Enjoy warm or at room temperature.