Remove puff pastry from the fridge and let it sit for 5 minutes to soften slightly. In a shallow bowl, whisk together the sugar, cinnamon, and salt until evenly combined.
Unfold the puff pastry on a lightly floured surface. Roll it gently to smooth any creases, then cut into 8 equal strips about 1 inch wide and 10 inches long.
Brush each strip lightly with the egg wash. Twist each strip by holding both ends and rotating in opposite directions 4-5 times, creating a spiral. Place on a parchment-lined baking sheet and refrigerate for 15 minutes.
Heat 1 tablespoon of vegetable oil in a large nonstick skillet over medium heat. Working in batches, cook the twisted pastries for 2-3 minutes per side until deep golden brown and puffed, adding more oil as needed between batches.
Immediately brush each hot pastry generously with melted butter on all sides, then roll in the cinnamon sugar mixture until completely coated.
Transfer to a wire rack and let cool for 5 minutes before serving. The exterior will crisp as they cool slightly.