Preheat the oven to 350 degrees F. Position racks in the upper and lower thirds of the oven. Line three baking sheets with parchment paper.
In a very small bowl, whisk together the chile paste, soybean paste, honey, mirin, 2 teaspoons crushed roasted sesame seeds, garlic powder and sesame oil until smooth. Set aside.
Lightly flour a clean work surface. Roll one piece of the puff pastry into a 10-by14-inch rectangle and set aside. Roll the other piece into a 10-by14-inch rectangle and spread with the chile paste mixture, leaving a 1/2-inch border. Set the first rectangle on top of the second, matching up the edges, and roll very gently to seal the pieces together.
Brush the pastry with egg wash--avoiding the edges so the layers of pastry don't stick together during baking--and sprinkle with 1 1/2 tablespoons of the remaining roasted sesame seeds and 1 1/2 tablespoons of the black sesame seeds. Lightly press the seeds in with your hands. Carefully flip the pastry over onto one of the prepared baking sheets, brush with more egg wash, and sprinkle with the remaining 1 1/2 tablespoons roasted sesame seeds and 1 1/2 tablespoons black sesame seeds, lightly pressing them in with your hands. Refrigerate for about 15 minutes, until firm enough to handle.
Using a pizza wheel or floured knife, trim the edges as needed to neaten them. Cut the pastry lengthwise into 1/2-inch strips. Gently twist each strip until it resembles a loose corkscrew. Transfer the strips to the prepared baking sheets, spaced about 1 1/2 inches apart. Chill for 20 minutes.
Bake until golden, 20 to 22 minutes, rotating the pans halfway through. Let the sesame straws cool on the baking sheets. Serve at room temperature.