Preheat the oven to 400°F or 200°C and line two baking trays with parchment. Cut the pie crusts into six circles about 6 inches wide.
Toss the sliced apples with granulated sugar, cinnamon, lemon juice, and flour. Stir gently so the slices remain intact.
Divide the apple mixture among the pastry circles, leaving a border of about 1 1/2 inches. Keep the filling fairly flat so it cooks evenly.
Fold the pastry border over the outer apples, creating overlapping pleats. Brush the visible fruit with melted butter.
Whisk the egg with water and brush it over the crust. Sprinkle coarse sugar around the edges for extra crunch and shine.
Bake for 22 to 27 minutes, until the crust is golden and the fruit is tender. Cool for 10 minutes before transferring the galettes from the tray.
