Add the onion, celery, and bell pepper to a food processor. Pulse until finely chopped, being careful not to puree the vegetables.
Heat the olive oil and butter in a large Dutch oven or soup pot over medium heat. Add the chopped vegetable mixture and cook for about 5 minutes, stirring occasionally, until softened and the onions are translucent.
Add the carrots, garlic, and ginger to the food processor and pulse until finely chopped.
Add the carrot mixture to the pot along with the turmeric and black pepper. Cook for another 2–3 minutes, stirring frequently.
Pour in the chicken broth and add the salt. Bring to a boil, then reduce to a steady simmer. Cook uncovered for 20–25 minutes, or until the vegetables are very tender.
Using a slotted spoon, remove about 2 cups of the vegetables and set aside.
Use an immersion blender or regular blender to blend the remaining soup until smooth and creamy.
Bring the soup back to a gentle boil and stir in the pastina. Reduce to a steady simmer and cook according to the package directions, stirring occasionally to prevent the pasta from sticking.
Stir in the shredded chicken, 1 can drained and rinsed white beans, reserved vegetables, and 4 large handfuls of fresh spinach. Cook for another 2–3 minutes, just until the spinach has wilted and everything is heated through.
Taste and adjust the seasoning, adding additional salt or pepper as needed. Serve topped with grated Parmesan.
