Carefully separate lettuce leaves, keeping them whole. Rinse and pat completely dry with clean kitchen towels or use a salad spinner. Set aside on serving platter.
Heat sesame oil in a large skillet over medium-high heat. Add ground chicken and break up with wooden spoon as it cooks, about 5-6 minutes until browned.
Add minced garlic, grated ginger, and white parts of green onions. Stir for 30 seconds until fragrant, being careful not to burn garlic.
Toss in diced red bell pepper and shredded carrots. Cook another 2-3 minutes until slightly softened but still crisp.
In small bowl, whisk together soy sauce, Thai sweet chili sauce, fish sauce, honey, and red pepper flakes.
Pour sauce mixture over chicken and vegetables. Stir to coat everything evenly. Simmer for 2-3 minutes, allowing flavors to meld.
Remove from heat. Stir in most of remaining cilantro and green onion tops, reserving some for garnish. Taste and adjust seasoning.
To serve, spoon chicken filling into lettuce cups. Garnish with reserved cilantro, crushed peanuts, and lime wedges on the side.