Warm a large skillet over medium-high heat. Add the olive oil. When hot, add the onion and cook 2–3 minutes until softened.
Stir in the garlic and ginger.
Cook 30 seconds until fragrant, being careful not to burn.
Add the ground turkey. Break it up with a spoon and cook 5–7 minutes until browned and no longer pink.
Mix in the bell pepper, mushrooms, and carrots. Cook another 3–4 minutes until the vegetables soften and any excess moisture cooks off.
In a small bowl, whisk together the soy sauce, rice vinegar, hoisin (or honey), sriracha, sesame oil, black pepper, and a pinch of salt.
Pour the sauce over the turkey mixture.
Stir and let it simmer 2–3 minutes to thicken slightly and coat everything evenly. Taste and adjust seasoning.
Remove from heat. Arrange lettuce leaves on a serving plate.
Spoon the turkey mixture into each leaf.
Top with green onions, cilantro, sesame seeds, and a squeeze of lime. Serve immediately while warm and crisp.