In a small mixing bowl, whisk together all of the sauce ingredients and set aside.
In a large (12-inch) skillet, heat one tablespoon of the canola oil over medium heat. Add the garlic and sauté until aromatic, about one minute.
Add the carrots and sauté until slightly softened, about five minutes. Add the shiitake and wood ear mushrooms and sauté until mushrooms have shrunken considerably, about 15 minutes. Don’t worry if some golden browned bits are beginning to stick to the skillet — the sauce will help you scrape those up later.
Scoot the sautéed vegetables to the edges of the skillet. Add the remaining tablespoon of canola oil to the skillet, then add the ground turkey breast on top of the oil, breaking it up with a spatula. Sauté the turkey until it is completely cooked through, continuing to break it up as it browns, about 10 minutes.
Add the reserved sauce and green onions to the skillet. Stir everything together until the turkey and vegetables are thoroughly mixed and coated evenly with sauce.
Spoon onto lettuce leaves and serve immediately. Alternately, you can serve bowls of the stir-fry with lettuce leaves alongside for your guests to assemble.