Put a large piece of parchment paper on a work surface and sprinkle with 2 tablespoons of the vanilla sugar. Lay the puff pastry on top, sprinkle with 2 more tablespoons vanilla sugar and roll out into a 12-inch square. Trim the edges to make an even square, then cut the pastry into four 3-inch-wide strips.
Lightly beat the egg and water in a small bowl. Brush the egg wash lengthwise down the center of 3 of the pastry strips. Stack the 3 strips neatly on top of each other; top with the remaining pastry strip. Place the rolling pin lengthwise down the center of the pastry stack and press gently to adhere the layers in the center; the edges should remain separated. Cut the stack crosswise into 1/2-by-3-inch strips. (If the pastry is too soft to cut, transfer to a baking sheet and refrigerate until firm, about 15 minutes.)
Line 2 baking sheets with parchment paper. Pinch the center of each strip, then twist the pastry twice at the pinch point. Arrange 1 inch apart on the prepared baking sheets. Fan out the edges of the pastry. Lightly brush with the egg wash, then sprinkle with the remaining 2 tablespoons vanilla sugar. Refrigerate until firm, about 20 minutes.
Position racks in the middle and lower thirds of the oven; preheat to 375 degrees F. Bake, switching the pans halfway through, until the cookies are golden brown, 18 to 20 minutes. Immediately transfer the cookies to racks to cool completely.
Photograph by Ryan Dausch