In a small bowl, whisk together the egg and heavy cream to make an egg wash. Set aside.
On a lightly floured surface, roll out the puff pastry to form a 12 1/2-inch-by-17 1/2-inch rectangle. Cut 1/2-inch strips from each side of the puff pastry. Transfer puff pastry rectangle to a baking sheet that has been sprinkled with water. Neatly brush a 1/2-inch wide border of water along each edge of the puff pastry rectangle. Top with corresponding strips of dough, pressing gently with your fingers to adhere. Using a fork or a docker, poke holes in the dough. Let stand at room temperature for 30 minutes. Transfer to refrigerator and chill for 1 hour.
Preheat oven to 400 degrees. Sprinkle chilled dough with 2 tablespoons sugar. Arrange plums on dough in overlapping rows. Sprinkle with remaining 1 1/2 tablespoons sugar and dot with butter. Brush edges with egg glaze. Place in oven and bake for 20 minutes. Rotate baking sheet in oven and continue baking until the edges are puffed and golden brown, 20 to 25 minutes more. Serve with ice cream, if desired.