2Meanwhile, cut squash into 4 wedges and remove seeds. Cut each wedge into 4 pieces. Add squash to stock and simmer until tender, 8–10 minutes. Add cabbage and cooked chicken and cook until warmed through, about 4 minutes. Season with salt and pepper.
3Divide soup among bowls. Top with jalapeño and some basil and cilantro; drizzle with chili oil and finish with a pinch of ginger. Serve with lime wedges for squeezing over.
4Do Ahead: Soup (without toppings) can be made 3 days ahead. Let cool; cover and chill. Can be frozen in individual servings – enough to see you through an entire season of colds and flu.