Heat the sesame oil in a large skillet over medium heat.
Add the shallot, carrots, and water chestnuts and cook, stirring occasionally, until the shallots begin to soften, about 2-3 minutes.
Season the ground beef with salt and pepper and add to the pan.
Cook, breaking up, until the meat is no longer pink in the center, about 5-7 minutes. Drain any excess grease from the pan.
In a separate bowl, combine the hoisin sauce, soy sauce, rice wine vinegar, garlic, and ginger. Mix well.
Add the sauce to the pan and stir to combine. Cook 1-2 minutes or until heated through.
Serve by filling leaves of lettuce with the ground beef mixture and top with sriracha, sesame seeds, and/or slices of green onions, if desired.