Peel and chop the butternut squash. Or, if you are using pre-peeled and chopped butternut squash, rinse it under cold water to remove any residue.
Add the olive oil to a large pot over medium heat on the stove. Then, add the diced onion and sauté, it will take about 5 minutes.
Add the chopped butternut squash, diced apples, mild curry powder, cinnamon, nutmeg, salt, and pepper. Cook these ingredients in the pot for about 10 minutes, stirring occasionally, until the squash and apples begin to soften.
Pour the unsweetened applesauce and chicken broth or vegetable broth into the pot. Then, mix the ingredients and bring the soup to a boil. Once boiling, reduce the heat to a simmer, place the lid on the pot, and let everything simmer for about 30 minutes, or until the butternut squash is completely tender.
Use an immersion blender to blend the soup until smooth. Or, let the soup cool, transfer it to a regular blender in batches, and blend.
Ladle the warm soup into bowls, add optional toppings such as roasted pumpkin seeds, and enjoy!