Add the remaining butter to the pan with the sliced shallots. Saute until golden-brown and crispy, 5-8 minutes. Meanwhile, cut the puff pastry down the middle and place both pieces 3-4 inches apart on the baking tray. Whisk the egg with a tablespoon of water, and brush the pastry sheets with egg. Neatly layer green beans down the length of each puff pastry rectangle.