In a small bowl, combine 1 tablespoon of soy sauce, cornstarch, and 2 tablespoons of water. Whisk until smooth and set aside.
In a large skillet or wok, heat the canola oil over medium-high heat. Add the ground turkey (or crumbled tofu) and cook until browned, breaking it apart with a spatula as it cooks. This should take about 5-7 minutes.
Once the turkey is browned, add the minced garlic, ginger, and sliced mushrooms to the skillet. Stir everything together and cook for another 2-3 minutes until the mushrooms begin to soften.
Add the broccoli coleslaw and grated carrots to the skillet. Pour in the remaining soy sauce, rice vinegar, chili paste, and sesame oil. Stir everything together and cook for an additional 3-4 minutes until the vegetables are tender but still crisp.
Pour the prepared sauce into the skillet and mix well. Cook for another minute or so until the sauce thickens and coats the vegetables and protein nicely.
Remove the skillet from heat, and season with ground black pepper to taste. Top with chopped green onions.