Prepare the lettuce. Wash the lettuce leaves carefully and pat them dry.
Set them aside in the refrigerator while you cook so they stay crisp.
Cook the beef. Heat the sesame oil in a large skillet over medium-high heat. Add the ground beef and cook until browned, breaking it up with a spoon as it cooks.
Add the onion, garlic, and ginger. Stir in the chopped onion and cook for 2 to 3 minutes until softened. Add the garlic and ginger, then cook for 30 seconds until fragrant.
Mix in the sauce. Add the soy sauce, hoisin sauce, rice vinegar, brown sugar, and sriracha if using.
Stir well so the beef gets fully coated.
Add the vegetables. Mix in the shredded carrots and chopped water chestnuts. Cook for another 2 to 3 minutes so the vegetables soften slightly but still keep some crunch.
Finish with green onions. Stir in the sliced green onions and remove the skillet from the heat. Taste and adjust with a little more soy sauce or sriracha if needed.
Assemble the wraps. Spoon the beef mixture into the lettuce leaves.
Top with sesame seeds if you like, and serve right away.