Add the water and cornstarch to a jar or medium bowl. Use a fork or small whisk to stir the mixture until the cornstarch dissolves.
Add the soy sauce, hoisin sauce, brown sugar, garlic, ginger, and crushed red pepper (if using). Stir vigorously until well combined. Stir the sauce again just before using.
Heat the oil in a large, deep skillet over medium-high heat.
Add the ground turkey to the skillet, breaking it up slightly and spreading it into a single layer. Cook for 2 minutes without stirring.
Stir the turkey while breaking it up further, then spread it into a single layer again. Cook for another 2 minutes.
Continue stirring and breaking up the turkey, cooking for 2–3 more minutes until it is browned and the liquid has evaporated. Stir frequently to prevent clumping.
Add the shredded cabbage mix to the skillet. Stir well to combine and cook for 1–2 minutes, stirring frequently.
Lower the heat to medium-low. Add the stir fry sauce and stir well to coat the turkey and cabbage evenly.
Cover the skillet and cook for 5 minutes to allow the flavors to meld, stirring occasionally.
Stir in the sliced green onions and serve with white rice or noodles, if desired.