Heat the olive oil in a large pot or skillet over medium heat. Add the diced onion and cook for about 5 minutes until it becomes soft and translucent. Stir in the minced garlic and grated ginger, cooking for another 1 minute until fragrant.
Add the curry powder, cumin, and turmeric to the pot. Stir constantly for about 30 seconds to 1 minute. Toasting the spices in oil helps release their essential oils, making the curry much more flavorful.
Whisk in the pumpkin puree, coconut milk, and vegetable broth. Stir until the mixture is smooth and the pumpkin is fully incorporated into the liquid. Bring the sauce to a gentle simmer over medium-low heat.
Add the drained chickpeas to the pot. Stir well to coat them in the pumpkin sauce. Let the curry simmer gently for about 10 minutes, allowing the sauce to thicken slightly and the chickpeas to heat through.
Stir in the fresh spinach or kale. Cook for 2 minutes until the greens have wilted. Turn off the heat and stir in the lime juice. Season with salt and pepper to taste. The lime juice is essential as it brightens all the heavy flavors.