Heat the vegetable oil in a large skillet over medium-high heat. Add the ground beef and cook until browned, about 5 minutes, breaking it apart with a wooden spoon or spatula.
Drain excess fat if necessary, then add the minced garlic, minced ginger, chopped onion, and bell pepper to the skillet. Sauté for an additional 2-3 minutes until vegetables are tender.
Stir in the shredded carrots, soy sauce, hoisin sauce, rice vinegar, sesame oil, and Sriracha (if using). Cook for another 2-3 minutes until everything is well combined and heated through.
While the beef mixture cooks, gently separate the leaves from the head of lettuce and rinse them under cold water. Pat them dry with a paper towel.
To serve, spoon some of the beef mixture into the center of each lettuce leaf. Top with sliced green onions and sprinkle with sesame seeds.
Serve immediately and enjoy wrapping the mixture in the fresh lettuce!