Inspired by: https://www.delish.com/cooking/recipe-ideas/a49533/copycat-pf-changs-lettuce-wraps-recipe/
Make the sauce: In a small bowl, whisk together hoisin sauce, soy sauce, vinegar, and sesame oil.
In a large skillet over medium-high heat, heat olive oil. Add onions and cook until very soft, around 5-7 minutes, then stir in garlic whites of green onions and cook until fragrant, 1 minute more. Add ground chicken and cook until opaque and mostly cooked through, breaking up meat with a wooden spoon. If not using cooking oil at the beginning of this step, have some chicken stock/broth on hand to periodically deglaze the pan as vegetables/chicken begin to stick. This works better if you have a well-seasoned wok or pan.
Pour in sauce and cook 1 to 2 minutes more, until sauce reduces slightly and chicken is cooked through completely. Turn off heat and stir in the rest of the green onions. Season with salt and pepper.
Spoon rice, if using, and a large scoop (about 1/4 cup) of chicken mixture into center of each lettuce leaf. Serve immediately.