Prepare the butternut squash by peeling, seeding, and cubing it into bite-sized pieces.
In a large pot, heat the vegetable oil over medium heat and sauté the diced onions until translucent, about 5 minutes.
Add the minced garlic and grated ginger to the pot, cooking for an additional 1-2 minutes until fragrant.
Stir in the curry powder, ground cumin, and turmeric, cooking for another minute to toast the spices.
Add the cubed butternut squash to the pot, stirring to coat it with the spices and aromatics.
Pour in the coconut milk and vegetable broth, then stir to combine all the ingredients well.
Bring the mixture to a boil, then reduce the heat and let it simmer for about 20–25 minutes, or until the squash is tender.
If using, add the chopped spinach or kale during the last 5 minutes of cooking, allowing it to wilt.
Season with salt to taste, adjusting as necessary, before serving.