In a large bowl, combine pecans, maple syrup, brown sugar, butter, and cinnamon, and stir with a wooden spoon to mix well.
Open thawed puff pastry on a large piece of parchment paper and roll slightly with a rolling pin to even out any creases and to slightly flatten it.
Spread filling mixture into the center third of the puff pastry, leaving a gap near the top and bottom.
Use a sharp knife or pizza cutter to slice diagonal cuts into the outer thirds of the pastry, leaving a one-inch gap between the cuts and the filling.
Fold the pastry strips over the middle, overlapping each other to create a braid pattern. Tuck the top and bottom in and pinch pastry anywhere there may be gaps.
Brush all over pastry with egg wash.
Place pastry and parchment on a baking sheet and bake in preheated oven for 25 minutes or until pastry is golden brown and filling is bubbling. Allow to cool before adding icing.
Add powdered sugar, vanilla, salt, and milk to a bowl and whisk to combine.
Whisk in additional milk, if needed, to achieve desired consistency. Icing should be thin but not overly runny.
Storage/Freezing: This pastry is best enjoyed the day it's made, since the puff pastry loses much of its flakiness in the fridge or freezer. But you can store leftovers in the fridge in an airtight container, and let thaw at room temperature still in the container to prevent condensation.