Preheat oven to 325°F. Score one side of steak in a crisscross pattern, making cuts 1/8” deep and 1” apart.
Sauté onion and celery in butter over moderately low heat 8 minutes until pale golden; off heat, mix in crumbs, 1 teaspoon salt, 1/8 teaspoon pepper, and the herbs. Sprinkle unscored side of steak with remaining salt and pepper and spread stuffing to within 1” of edges, patting down firmly. Roll jelly-roll style, starting from a short side, and tie well with string (around the roll and end over end).
Brown roll in drippings in a Dutch oven over moderate heat 7-10 minutes, add broth, cover, and bake 1½ hours until tender. Transfer meat to a platter and remove strings.
Mix flour-water paste into pan liquid and heat, stirring, until thickened. Cut steak crosswise into thick slices and serve with gravy.
Argentine Stuffed Flank Steak: Score steak as directed above, then prepare the following stuffing: remove casings from ½ pound chorizo or other garlic-flavored sausage and Sauté the meat, breaking it up, 5 minutes over moderately high heat. Add ½ cup minced celery and 4 minced scallions and Sauté 5 minutes longer. Off heat mix in ½ cup soft white bread crumbs, ¼ cup minced parsley, ½ teaspoon salt, and 1 lightly beaten egg. Spread on steak as directed above, then roll, brown, and bake as directed. Serve with a peppery chili sauce.