1/2 (17.3 ounce) package frozen puff pastry sheets (1 sheet)
1 1/3 cups grated Parmesan cheese
2 tablespoons everything bagel sesame seasoning blend
1 large egg, lightly beaten
1 scant tablespoon all-purpose flour
1/4 cup ketchup, or as needed for dipping (optional)
3 tablespoons Dijon mustard, or as needed for dipping (optional)
Thaw puff pastry at room temperature until just pliable, about 1 hour, or according to package directions.
Preheat the oven to 400 degrees F (200 degrees C). Line a 12x18-inch sheet pan with parchment paper.
Sprinkle the parchment paper with 1/2 the cheese and 1/2 the seasoning blend, in an area about the same size as the puff pastry sheet.
Brush one side of pastry with beaten egg, and lay pastry in the prepared pan, egg-wash-side down.
Lightly flour a rolling pin, allowing any excess to fall on pastry. Roll pastry to press seasoning and cheese into the bottom of pastry sheet.
With a sharp knife or bench scraper, cut pastry lengthwise into 9 strips, and then cut strips in half crosswise, to make a total of 18 strips.
Brush tops of pastry strips with egg wash, then sprinkle with remaining Parmesan and seasoning blend. Lift the ends of each strip and gently twist; arrange twists on the pan, leaving space between them.
Bake in the center of the preheated oven until browned, about 10 minutes. Remove the pan from the oven, and use tongs to turn each twist over; bake 5 minutes more.
Remove from the oven to cool slightly on a rack. Serve warm, as bread sticks with a meal, or as appetizers, with ketchup and Dijon mustard for dipping.
