Rinse the meat and pat dry and place in a sealable plastic bag or small glass dish. In a medium bowl, combine 1 tablespoon of the lime juice, the soy sauce, oil, brown sugar, garlic, ginger, and red curry paste. Pour half the mixture into the bag with the meat. Add the remaining 2 tablespoons lime juice to the bag. Seal tightly and marinate the meat in the refrigerator for at least 4 hours or overnight, turning occasionally. Reserve the rest of the mixture to dress the salad.

Coat a grate or a grill pan with cooking spray and preheat over medium-high heat until hot. Grill the steak until medium-rare, about 5 minutes per side, or to your desired degree of done ness. Let it rest for 5 minutes until room temperature, then slice thinly against the grain.

Combine the lettuce, shallots (reserving a few slices for garnish), cilantro, basil, and beef in a large salad bowl. Add the reserved dressing and toss to coat. Divide the salad among 4 plates and garnish with the sliced shallots.