Heat vegetable oil in a large skillet over medium-high heat. Add minced garlic and ginger, stirring constantly for 30 seconds until fragrant.
Add ground turkey to the skillet, breaking it up with a wooden spoon. Cook for 6-8 minutes, stirring frequently, until turkey is browned and cooked through.
In a small bowl, whisk together hoisin sauce, soy sauce, sriracha, and sesame oil. Pour sauce over the cooked turkey and stir to combine.
Cook for an additional 2-3 minutes, stirring frequently, until sauce is heated through and turkey is well coated. Remove from heat.
Arrange clean, dry lettuce leaves on a serving platter. Spoon warm turkey mixture into lettuce cups.
Garnish with sliced green onions, chopped cilantro, and sesame seeds. Serve immediately while turkey is still warm.
Notes
Storage tip: Turkey mixture keeps in refrigerator for up to 4 days. Reheat gently in skillet with splash of broth. Prepare lettuce cups fresh for best texture.