Butterfly flank with the grain to 1/4-inch thick, yielding about an 11-by-14-inch rectangle. Place in a shallow baking dish with balsamic vinegar. Cover with plastic wrap and refrigerate.
In a food processor, pulse together walnuts, 3 tablespoons parmesan, garlic, red pepper flakes and 1 teaspoon salt to the consistency of coarse cornmeal. Add olive oil while blending to make a paste; set aside.
Preheat oven to 450 degrees. Remove flank, pat dry and lay flat on a cutting board. Layer with walnut paste, arugula and sun-dried tomatoes. Roll and tie roast to the 11-inch length.
Season the exterior evenly with remaining 2 tablespoons parmesan, 1 teaspoon salt, rosemary and pepper. Set in roasting pan with rack, uncovered. Roast for 10 minutes. Reduce heat to 325 and roast an additional 60 minutes for medium rare.
Allow to rest 10 minutes before slicing, two slices per person.