Make the sauce: in a jar or bowl combine 1/3 cup hoisin, 1/3 cup tamari or soy sauce, 2 tablespoons vinegar, 1 tablespoon chili paste, 4 chopped garlic cloves, 1 teaspoon ground ginger, a pinch of black pepper and chili flakes, and 1/3 cup water; stir or shake until smooth.
Cook the noodles according to package directions until just tender (about 2–3 minutes for fresh-style ramen); drain and set aside.
Season the chicken: in a large bowl toss the cubed chicken with 1 tablespoon garlic powder, 1/2 teaspoon ground ginger, a pinch of black pepper, 3 tablespoons arrowroot powder or cornstarch, and 2 tablespoons tamari or soy sauce until evenly coated.
Heat 3 tablespoons sesame oil in a large skillet over medium-high heat. Add the chicken and cook, stirring occasionally, until browned and cooked through, about 6–8 minutes.
Add the cashews to the skillet and cook for 1–2 minutes more until they are golden and toasted.
Pour the prepared sauce over the chicken and cashews and cook, stirring, until the sauce thickens slightly and coats the chicken, about 1–2 minutes.
Add the drained noodles to the skillet and toss thoroughly to coat with the sauce. Remove from heat.
Serve immediately topped with chopped green onions and additional black pepper or chili flakes if desired.
