Dust a large cutting board or your kitchen counter lightly with flour. Unroll the sheet of puff pastry carefully; if it sticks to itself or seems gummy, stop and put it back in the refrigerator for a few minutes to firm up.
Cut the puff pastry lengthwise to make two rectangles. Set one rectangle aside (or roll it up again and store it in the fridge) for another use.
Carefully slice the smoked duck breast crosswise (i.e., along the short side) into thin slices.
Using a pastry brush, brush the mango chutney up the center of the rectangle in a 2-inch wide stripe. Lay the slices of smoked duck breast in a slight diagonal over the mango chutney, slightly overlapping each slice with the previous slice you put down. Continue until the pastry is covered in duck breast up the center in a single row.
Using a sharp paring knife, carefully cut diagonal, ½ inch strips on each side of the duck breast. Carefully fold one strip on the right side over the duck breast, followed by one strip on the left side of the duck breast. Continue until al of the strips have been folded up and over the duck breast.
Brush the egg over the pastry with a pastry brush. Slide the entire puff pastry into the oven and bake for 20 minutes until puffed and golden. Serve immediately.
Recipe by Grits and Chopsticks at https://www.gritsandchopsticks.com/the-gravy-train/2017/11/braided-smoked-duck-pastry-sponsored-by-les-petits-cochons.html