While you're gathering ingredients, prepare all your components for quick assembly. Mince the garlic cloves fresh (this releases the most aromatic oils), slice the green onions into 1/4-inch rounds, and dice the water chestnuts into uniform 1/4-inch pieces—uniform sizing ensures consistent texture in every bite. In a small bowl, whisk together the hoisin sauce, soy sauce, rice vinegar, and chili paste until smooth. Having everything prepped and your sauce ready means the cooking process will move quickly without any stalling.
Heat the olive oil in a large skillet over medium-high heat until it shimmers, then add the ground turkey and break it apart with a wooden spoon, stirring frequently. After about 2-3 minutes, once the turkey has lost most of its pink color, add the minced garlic and ginger and cook for another 3-4 minutes, stirring constantly. This timing allows the aromatics to bloom and infuse the turkey with flavor while the meat finishes cooking through. I like using Butterball ground turkey because it has a leaner, cleaner flavor that lets the Asian seasonings shine through without any gamey notes.
Add the green onions and diced water chestnuts to the cooked turkey mixture and stir well to combine, cooking for about 1 minute so the water chestnuts warm through and soften slightly. Pour in the sauce mixture from Step 1 and stir everything together until the filling is evenly coated and the ingredients are well combined. Add a pinch of salt to taste, then finish with the sesame oil, stirring gently to incorporate its nutty aroma throughout. The whole filling should look glossy and cohesive, with the sauce clinging to every piece.
Arrange the lettuce leaves on a serving platter and spoon approximately 1/4 cup of the warm turkey filling into each leaf. I recommend serving the wraps immediately while the filling is still warm and the lettuce is crisp—the contrast between the hot, savory filling and the cool, fresh crunch of the lettuce is what makes this dish so satisfying. You can set out extra sauce on the side for anyone who wants to drizzle more, or let guests customize their wraps by adding extra green onions or water chestnuts.