Preheat oven to 425°; line rimmed baking pan with parchment paper. Lightly dust cutting board with flour; thaw puff pastry sheet as label directs on cutting board.
Steam green beans in microwave oven as label directs. Divide green beans into 8 bundles; wrap each bundle with 1 slice prosciutto.
In small bowl, whisk egg and 1 tablespoon water.
Gently roll puff pastry into 10-inch square; cut into 8 (2 ½ x 5-inch) rectangles. Brush egg mixture over rectangles; sprinkle with ½ cup cheese. Place 1 green bean bundle at short end of each rectangle; tightly roll up each pastry, pressing to seal. Transfer bundles, seam side down, to prepared pan.
Brush each puff pastry with egg mixture and sprinkle with remaining ¼ cup cheese; bake 15 minutes or until golden brown. Makes 8 bundles.