Cut the squash into 1-inch cubes and add to a sheet pan along with the onion. Toss with 2 tablespoons of the oil and season with salt and black pepper. Roast until the squash and onion are caramelized and softened, 30 to 35 minutes.
Meanwhile, place a large saucepan over medium heat. Add in the remaining 2 teaspoons oil along with the chickpeas, ginger, curry powder, cumin, turmeric, coriander, cayenne pepper and garlic. Season with salt and black pepper and cook, stirring frequently, for 1 to 2 minutes to toast the spices and bring the flavors together.
Stir in the tomato paste and cook for an additional minute.
Add in a splash of the broth to deglaze the pan, scraping the bottom to lift off any stuck-on bits. Stir in the remaining broth followed by the coconut milk and bring to a simmer.
Add in the kale and cook until tender, about 5 minutes.
Remove the squash and onions from the oven and, using a fork, mash about half of the squash. Add the mashed squash along with the unmashed squash and onions to the pot and stir through the stew to thicken. Simmer for at least 2 minutes to bring the flavors together.
Finish with the lemon juice and a final seasoning of salt and black pepper, if needed.
Serve the stew topped with some yogurt and cilantro if desired.