Prepare the Dough: In a large bowl, whisk together the 1.5 cups of flour, 1 teaspoon sugar, and salt. Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs with some pea-sized bits of butter remaining.

Add the ice water one tablespoon at a time, mixing until the dough just comes together. Do not overwork. Form the dough into a flat disk, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes.

Prepare the Filling: In a separate bowl, gently toss the sliced plums with 1/4 cup sugar, cinnamon, and 1 tablespoon of flour until evenly coated. Set aside.

Assemble the Galette: Preheat oven to 400°F (200°C). On a lightly floured surface, roll the chilled dough into a rough circle, about 1/8 inch thick and roughly 14 inches in diameter. Transfer the dough to a parchment-lined baking sheet.

Arrange the plums in the center of the dough, leaving a 2-inch border all the way around. Fold the dough border up and over the edges of the fruit, creating pleats as you go to form the rustic edge.

Brush the folded edges of the dough generously with the beaten egg wash and sprinkle evenly with the coarse sugar.

Bake for 40 to 45 minutes, or until the crust is deeply golden brown and the plum juices are bubbling thickly. Let cool on the baking sheet for at least 15 minutes before slicing and serving warm.