Place noodles in a large bowl. Cover with boiling water; let stand 20 minutes. Drain and rinse with cold water; drain.
Heat oil in a wok or large skillet over medium-high heat. Add onion, ginger, curry powder, and garlic to pan; stir-fry 3 minutes. Add carrot; stir-fry 1 1/2 minutes. Add cabbage and 1 1/2 tablespoons water; cook 2 minutes, stirring often. Remove from heat.
Combine cilantro and next 5 ingredients (through pepper) in a bowl, stirring until sugar dissolves. Add the noodles, cilantro mixture, and 1 1/2 cups bean sprouts to pan; toss to combine. Spoon 1/3 cup noodle mixture on each lettuce leaf; roll up.