In a medium mixing bowl, whisk together 1 tablespoon soy sauce and cornstarch with a fork. Add the turkey, breaking apart the meat and stirring to coat with the sauce. Let marinate 10 minutes.
Heat a wok or large, deep sauté pan over high heat. Add the oil and swirl to coat. Add the marinated turkey and cook, breaking apart the meat into small bits with a heatproof spatula, until it's no longer pink and fully cooked through, about 5 minutes. Add the green onions (reserve a small handful for serving) and mushrooms and cook until the mushrooms soften, about 2 additional minutes.
Reduce the heat to medium low. Add the broccoli coleslaw, carrots, ginger, and garlic. Stir-fry for 2 minutes, until the vegetables are softened.
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