In a large skillet, heat the sesame oil over medium heat. Add the minced garlic and grated ginger, sautéing for about 1 minute until fragrant.
Add the ground chicken or turkey to the skillet. Cook, breaking it apart with a spatula, until browned and cooked through, approximately 5-7 minutes.
Stir in the chopped water chestnuts, soy sauce, rice vinegar, and sriracha if using. Cook for an additional 2-3 minutes, allowing the flavors to meld together.
Remove the skillet from heat and fold in the chopped cilantro. Taste and adjust seasoning if needed.
To serve, spoon a generous amount of the filling into each lettuce leaf. Garnish with chopped peanuts or cashews if desired.
Arrange the filled lettuce cups on a serving platter and enjoy immediately.