Heat the olive oil in a large skillet over medium heat. Let it warm up for a minute.
Add the ground turkey to the pan. Let it cook untouched for about a minute, then break it up and cook until mostly browned.
Push the turkey to one side of the pan. Add the chopped onion and cook until softened, about 2 to 3 minutes.
Add the garlic and ginger. Stir everything together and cook until fragrant, about 30 seconds.
Stir in the soy sauce, hoisin or honey, sesame oil, rice vinegar, and chili paste if using.
Let the mixture simmer for a few minutes until the sauce thickens slightly and coats the turkey.
Taste and adjust seasoning if needed. Add more salt, heat, or sweetness as you like.
Spoon the turkey mixture into lettuce leaves and serve immediately.