In a large stockpot set over medium heat, add butter. Add onion, shallot, carrot, and celery, sauté for 5 minutes or until the vegetables are soft. Add the garlic and sauté for an additional 2 minutes, or until fragrant, stirring occasionally to prevent it from burning.
Whisk in the flour and cook for 1 minute. Gradually add in the chicken broth, then milk, whisk to combine. Add salt, Italian seasoning, thyme, pepper, and paprika. Continue cooking until the mixture reaches a simmer, then reduce heat to medium-low and simmer for 5 minutes.
Add the rotisserie chicken and spinach and gnocchi. Stir continuously for 1 minute, then simmer for 4 additional minutes. Remove from heat and serve.