Grill beef on an oiled rack set 5 to 6 inches over glowing coals 5 to 8 minutes on each side for medium-rare. (Alternatively, use a grill pan and grill 4 to 6 minutes per side.) Transfer beef to a cutting board and cool 30 minutes. Cut beef across 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).

Add beef, shallots, scallions, carrot, coriander and mint and toss well. Cut cucumber in half lengthwise and thinly slice.

Mound the salad in the center of the bowl and arrange cucumber around edge. Garnish with coriander sprigs and serve with rice.