Heat olive oil in a large skillet over medium heat. Add chopped onion and garlic, sauté for 2-3 minutes until softened.
Add ground chicken to the skillet, breaking it apart with a spatula. Cook until browned and cooked through, about 5-7 minutes.
Stir in diced red bell pepper, chopped mushrooms, and grated carrot. Cook for an additional 3-4 minutes until vegetables are tender.
Add soy sauce, hoisin sauce, and grated ginger to the skillet. Mix well and cook for another 2 minutes, allowing flavors to meld.
Remove from heat and let cool slightly. Spoon the chicken mixture into lettuce leaves, topping with sliced green onions and sesame seeds if desired.
Serve immediately, or refrigerate the filling for up to 2 days for a quick meal.