Place squash, onion, and garlic into a large rimmed skillet. Add oil and cook for about 2 minutes until onion softened.
While the squash cooks, whisk together curry paste, curry powder, coconut milk, broth, soy sauce, and ginger.
Add chickpeas and stir.
Add the curry liquid to the skillet and stir.
Allow curry to lightly simmer over medium-low heat until the squash is tender, about 20 minutes.
During the last 5 minutes of cooking, stir in the spinach. Season with salt and pepper to taste.
Serve over rice with lime wedges (optional), and top with chopped fresh cilantro.