In a large skillet over medium-high heat, heat the oil. Stir-fry the ginger for 30 seconds, then add the chicken and cook through, about 5 minutes.
Add the carrots, onion, broccoli, and cabbage and stir-fry until the cabbage is wilted, about 10 minutes. Add the spaghetti squash and sesame oil and mix well.
Combine the aminos, no-tomato sauce, and honey until well mixed, then add to the veggies and chicken and toss to coat before serving.