In a large pot, melt butter with olive oil over medium heat. Add onion and celery, cooking until softened, about 5 minutes. Add garlic and cook for 1 minute more.
Sprinkle flour over the vegetables and stir constantly for 2 minutes to create a roux. Gradually whisk in chicken broth, stirring to prevent lumps.
Add heavy cream, thyme, nutmeg, salt, and pepper. Bring to a gentle simmer and cook for 10 minutes, stirring occasionally.
Meanwhile, cook gnocchi according to package directions in a separate pot. Drain and set aside.
Add shredded chicken to the soup and heat through for 3-4 minutes.
Stir in spinach and cook until wilted, about 2 minutes. Add cooked gnocchi just before serving and stir gently to combine.