Heat a few tablespoons of olive oil (or other cooking oil of your choice) in a large pot over medium-high heat; once hot, add the onion, garlic, carrots and ginger. (If you are using fresh cubed squash, you will want to add it to the pot now as well)
Cook until slightly softened and fragrant, then add the salt, pepper and ground turmeric and stir well; continue cooking for a minute or two, to develop the flavors.
Add the vegetable broth, bring to a boil, then reduce the heat to a simmer and cook gently until the carrots are tender, about 5 minutes.
Add the cooked squash and continue cooking for about one minute, until the squash is heated through.
Carefully ladle the soup into a High-Speed Blender and process until smooth and creamy; work in batches if you have to.
Serve promptly, garnished with a few drops of toasted sesame oil, sesame seeds, chopped cilantro and finely chopped carrots, if desired.
This soup is also delicious served cold or at room temperature; feel free to experiment and decide which version you like best!
*Ginger does have a bit of an intense bite to it, and combined with the black pepper and turmeric, it gives this soup a serious kick! If you're not a fan of heat, you might want to start with less ginger and maybe consider leaving the ground black pepper out. You can always adjust later, if needed. **You could also use uncooked squash, peeled and cut into small cubes. You'll need about 4 cups. I used a combination of butternut and spaghetti squash, but practically any squash variety would work just fine.