Preparation

Make the filling

• Position a rack 5 to 6 inches from the broiler element and heat the broiler on high. Halve each pepper lengthwise and remove the seeds. Put the peppers skin side up on a large rimmed baking sheet lined with foil. Broil until the skin blackens, 20 to 25 minutes. Place the peppers in a zip-top plastic bag, seal, and let cool slightly, about 15 minutes. Rub the skin off using a paper towel.
• Put the peppers, relish, syrup, garlic, and bread in a food processor, and process until smooth. Put the mixture in a medium bowl, add the walnuts, and season to taste with salt and pepper.

Assemble the pinwheels

• Lay out a damp kitchen towel and cover with a sheet of plastic wrap. Unroll the phyllo on top of the plastic, and immediately cover with a second sheet of plastic wrap and another damp kitchen towel.
• Remove 2 sheets of phyllo, and place them on a work surface. Lightly brush the top sheet with melted butter. Cover with another 2 sheets of phyllo, brush again with butter, then add a final sheet of phyllo. Spread half of the filling in an even layer on top. Beginning at the long end, roll the phyllo tightly and brush the roll with butter. Wrap in plastic wrap and refrigerate until firm, about 1 hour, or freeze for about 30 minutes. Repeat to make a second roll.
• Position a rack in the top third of the oven and heat to 400°F. Line two large rimmed baking sheets with parchment paper. With a sharp knife, trim the ends from the rolls and cut each into 20 slices. Transfer the pinwheels to the prepared baking sheets and bake until golden, 10 to 12 minutes. Transfer the baking sheets to a wire rack and allow to cool. Serve warm or at room temperature, topped with the arugula.