Preheat the oven to 400°F (convection) and line your baking sheet with parchment paper.
In a saucepan, whisk together the milk, sugar, and vanilla pudding mix. Bring to a boil over medium heat, stirring constantly, until the pudding thickens. Set aside and let it cool slightly.
Unroll both puff pastry sheets and place them on the baking sheet. Spread the cooled pudding evenly over one of the puff pastry sheets.
Gently place the second sheet of puff pastry over the pudding layer. Press the edges lightly to seal, making sure no pudding spills out the sides.
Using a pizza cutter or a large, sharp knife, cut the layered puff pastry into approximately 20 strips.
Twist each strip. In a small bowl, whisk the egg. Brush the puff pastry pudding sticks with the whisked egg and sprinkle generously with cinnamon sugar.
Bake for 25 minutes, or until golden brown and puffed up.
Let cool slightly before serving.
