Heat olive oil and butter in a large soup pot over medium-high heat. Add onion, carrots, and celery stalks, then season with Kosher salt and black pepper. Cook, stirring occasionally, until translucent. Add chopped garlic, chopped rosemary, fresh thyme leaves, and curry powder, then cook.
Add flour. Cook, stirring constantly, until the flour has absorbed all the liquid.
Continue to stir until the flour has fully dissolved and no lumps remain. Add shredded rotisserie chicken and a Parmesan rind (if using). Simmer.
Carefully lower potato gnocchi into the soup along withbaby spinach and milk. Stir well, then cook until the gnocchi begin to float to the top. Taste, adjust seasoning as needed, then serve immediately with freshly shaved Parmesan, lots of cracked black pepper, and baguette.