Heat 1 tablespoon of olive oil in a large pot over medium heat.
Add the ground turkey to the pot and cook, breaking it up with a spoon, until browned and cooked through, about 6-8 minutes. Remove the turkey from the pot and set aside.
In the same pot, add the remaining 1 tablespoon of olive oil.
Add the diced onion and cook until softened and translucent, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Add the cubed butternut squash to the pot and stir to combine.
Sprinkle the ground cumin, ground cinnamon, and ground nutmeg over the squash and stir well.
Pour in the chicken broth and water, then bring the mixture to a boil.
Reduce heat to low, cover, and simmer until the butternut squash is tender, about 20 minutes.
Use an immersion blender to puree the soup until smooth. Alternatively, carefully transfer the soup in batches to a blender and puree until smooth, then return to the pot.
Return the cooked ground turkey to the pot and stir to combine.
Season the soup with salt and black pepper to taste.
Heat the soup gently for 5 more minutes to allow flavors to meld.
Ladle the soup into bowls and garnish with chopped fresh parsley before serving.