Start a charcoal or wood fire or preheat a gas grill or broiler; the rack should be about 4 inches from the heat source. Grill or broil the beef until medium-rare, 5 to 10 minutes; set it aside to cool.
Toss the lettuce with the mint, onion, and cucumber. Combine the remaining ingredients with 1 tablespoon water—the mixture will be thin—and toss the greens with