Bring 1 inch of water to a boil in a Dutch oven.
Meanwhile, slice steak in half lengthwise. Cut each half crosswise into 8 strips. Place each strip, cut side up, between 2 pieces of plastic wrap and pound with the smooth side of a meat mallet or a heavy saucepan until flattened to about 1/8 inch thick. Place the beef in a shallow glass or ceramic baking dish.
Whisk broth, soy sauce, brown sugar, vinegar, sherry, sesame oil, chile-garlic sauce and garlic in a medium bowl until the sugar has dissolved. Pour the mixture over the beef, turning to coat. Let marinate 10 minutes.
Add asparagus to the boiling water and simmer over medium heat for 2 minutes. Add scallions and cook for 1 minute more. Drain and rinse with cool water. Cut the asparagus in half. Cut the scallions in half crosswise, then lengthwise. Slice bell pepper into 32 thin strips.
Place rack in upper third of oven; preheat broiler. Line a baking sheet with foil.
To prepare rolls, lay a strip of beef on a work surface. Place 2 pieces of asparagus, 2 pieces of scallion and 2 pieces of bell pepper crosswise on the beef. Roll the beef around the vegetables. Place the roll, seam-side down, on the prepared baking sheet. Continue with the remaining beef and vegetables, making 16 rolls total. Transfer the remaining marinade to a small saucepan.
Broil the rolls until the beef is cooked through, 8 to 10 minutes.
Meanwhile, bring the marinade to a boil over high heat. Reduce heat to medium and simmer for 5 minutes. Serve rolls topped with the reduced marinade.
Ingredient note: Chile-garlic sauce (or chili-garlic sauce, or paste) is a blend of ground chiles, garlic and vinegar and is commonly used to add heat and flavor to Asian soups, sauces and stir-fries. It can be found in the Asian section of large supermarkets and will keep for up to 1 year in the refrigerator.