In a wok over medium-high, heat 1 tablespoon sesame oil. Brown white part of scallion, 2 minutes; add garlic, chili, carrot, and ginger, stirring frequently, until garlic is soft, 5 minutes. Add ground beef and brown, 2 to 3 minutes. Stir in tamari, fish sauce, chili paste (if using), and half the cilantro leaves; continue to cook until meat is hot and fragrant, 3 to 4 minutes.
Remove from heat, stir in juice from the lime, and add tamari to taste. Serve beef mixture in lettuce leaves sprinkled with bean sprouts, remaining cilantro leaves, and scallion.
Photography by Julia Gartland