Heat 1 tbsp olive oil in a large, high-sided skillet or wok over medium-high heat until shimmering.
Add 1 lb Jennie-O extra lean ground turkey breast to the skillet. Cook, breaking the meat up with a wooden spoon, until no longer pink (about 5–7 minutes).
Add 2 cloves garlic, minced, and 1 tsp ginger, minced, to the turkey. Cook 30–60 seconds, stirring, until fragrant. If any excess liquid or fat collects, carefully drain it from the pan.
Add 8 oz diced white button mushrooms, 8 oz drained and diced water chestnuts, and 5 diced green onions. Cook, stirring occasionally, until the mushrooms are tender, about 3–5 minutes.
Stir in 1 cilantro (leaves only, chopped), 3 tbsp soy sauce, 1/2 cup hoisin sauce, and 1 tbsp Sriracha. Cook 1–2 minutes more, stirring, until the mixture is heated through and the sauce coats the ingredients.
To serve, spoon the turkey mixture into butter lettuce leaves. Add hot cooked white rice to each wrap as desired, garnish with extra diced green onions, and drizzle additional Sriracha if you like.