Preheat the oven to 375 degrees F. Line a sheet pan with parchment.
Lay out the puff pastry on a lightly floured surface. Imagine the pastry has 3 equal sections. Add the hazelnut spread to the center section and, using a knife, cover the center section with the spread, leaving a 1/2-inch border at the top and bottom. Sprinkle the peanuts over the chocolate hazelnut spread.
Using a sharp knife, cut the 2 outside sections into six 1-inch horizontal strips just to the center section.
Fold the 1/2-inch borders at the top and bottom inwards, over the edges of the chocolate filling. Next, starting at one end, begin folding the pastry strips over the filling, alternating the sides to create a braid appearance. Put the braid on the parchment-lined sheet pan.
Brush the pastry braid with the beaten egg and sprinkle with the sea salt. Bake until golden and cooked through, 28 to 30 minutes.
While the pastry bakes, make the icing by whisking the powdered sugar, vanilla and milk in a bowl until smooth. Set aside.
Allow the pastry to cool for 10 to 15 minutes. Drizzle over the icing, slice and serve.