Preheat broiler or prepare grill.
Rub flank steak with black pepper, pressing it into meat. Grill steak on an oiled rack of a broiler pan, about 3 to 5 inches from heat 6 to 7 minutes on each side for medium rare. Or, grill over glowing coals 5 to 8 minutes on each side for medium rare. Transfer steak to a cutting board and cool. If desired, chill beef, loosely wrapped, at least 2 hours and up to 1 day to facilitate thin slicing. Cut beef across the grain into very thin slices.
In a large bowl stir together lime juice, fish sauce, sugar, and chilies until combined well (sugar should be dissolved if using).
Add steak, shallots, scallions, coriander and mint and toss well. Score cucumber lengthwise with tines of a fork and cut crosswise into thin slices.
Arrange cucumber around edge of a platter and mound beef salad in center. Garnish with coriander sprigs.