Preheat the oven to 375˚ F. Line a baking sheet with parchment paper. Cut the puff pastry sheet in half crosswise, then cut each half into nine 1-inch-wide strips and twist each strip a few times. Transfer to the baking sheet, brush each twist with the beaten egg and sprinkle with the everything bagel seasoning. Bake for 18 minutes, then rotate the pan and continue baking until the pastry is golden brown, another 4 minutes. Let cool.