Thaw puff pastry at room temperature for 40-45 minutes. Preheat oven to 375° F. Line baking sheet with parchment paper.
For the Buffalo Chicken Dip
Meanwhile, prepare buffalo chicken dip. In a medium pan over medium heat, combine cream cheese, Monterey Jack cheese, ranch dressing and Frank's Hot Sauce. Stir until melted and fulled combined. Remove from heat and fold in shredded chicken. Cool.
Unfold pastry sheets. Generously fill center third of each sheet with cooled buffalo chicken dip. Sprinkle each with half the sliced scallions and 1/4 cup crumbled blue cheese.
Using a pairing knife, cut 12 strips into the left and right thirds of each pastry sheet, as shown in the images above. Alternate folding strips over filling, creating a 'braid'. Trim last strips if necessary. Brush tops with beaten egg.
Bake at 375° F. for 35-40 minutes until tops of pastry is golden brown. Allow to cool slightly. Slice and enjoy!