Heat the oil in a large, heavy-bottomed pot over medium high heat. Add the onion and carrot. Sauté for 7 minutes, or until the onions are clear and the carrots are soft. Add the garlic and cook, stirring frequently, for another 2 minutes.
Add the squash, split peas, broth, curry powder, turmeric, cumin, salt, and pepper to the pot, along with 2 cups of water. Bring everything to a boil and reduce to a simmer.
Cover and simmer the soup for 1 hour, or until the split peas are tender (they’ll still retain their shape). Uncover, taste, and adjust the salt and pepper as needed.
You can serve the soup chunky or use an immersion blender to blend it partially or entirely. Serve, with a spoonful of vegan sour cream or unsweetened vegan yogurt if desired.