Preheat the oven to 400 degrees F (200 degrees C). Adjust an oven rack to the middle position. Butter two (6 to 8-ounce) ramekins and dust with white sugar.

Place apple slices on a microwave-safe plate, overlapping slightly if necessary. Microwave on high until slices slightly soften, about 45 seconds. Cover the plate with plastic wrap and a kitchen towel.

Mix together sugar and cinnamon in a small bowl.

Roll puff pastry sheet to less than 1/8-inch thickness. Using a pizza cutter, cut two (3x12-inch) rectangles. Reserve remaining pieces for another use.

Spread melted butter over dough; sprinkle with a generous amount of cinnamon sugar. Place apple slices along one long edge of dough, about 1/4 inch beyond the edge, overlapping slices slightly. Fold the bottom half of dough over apple slices to form a long "folder" of dough with rounded edges of apple slices exposed.

Beat together egg and water in a small bowl. Brush surface of dough with egg wash. Sprinkle with cinnamon sugar.

Starting at one end, roll dough to form a rose-shaped pastry. Seal roll with end of dough strip. Transfer roses to the prepared ramekins. Sprinkle with cinnamon sugar.

Bake on the middle rack in the preheated oven until well browned, about 45 minutes. Use tongs to remove the ramekins to a baking sheet to cool for 5 to 10 minutes. Remove apple roses from the ramekins and finish cooling on a wire rack. Dust with confectioners' sugar before serving.