Preheat the oven to 400 degrees F. Line 2 rimmed baking sheets with parchment paper or silicone baking mats.
Carefully unfold one puff pastry sheet onto a cutting board and brush with the melted butter.
Sprinkle with 1/4 cup Parmesan and 1/2 tablespoon rosemary. Add a dash of garlic powder and sprinkle salt across the length of the pastry.
Fold the sheet in half, lengthwise. Brush the top of the folded sheet with the beaten egg and sprinkle with 1/4 cup Parmesan, 1/2 tablespoon rosemary, a dash of garlic powder and a sprinkle with salt.
Cut the pastry into 1/2-inch strips with a knife or pizza cutter.
Twist the strips at each end in opposite directions to create a spiral effect. Stretch each strip slightly and pinch each end as you place the strip onto one of the prepared baking sheets, about 1 inch apart.
Repeat with the remaining puff pastry sheet, melted butter, Parmesan, rosemary, garlic powder, salt and egg.
Bake until the straws are lightly browned, 10 to 12 minutes.
Remove from the oven and allow to cool for 2 minutes before serving.