In a large pot, heat olive oil over medium heat. Add onion, celery, and carrot and sauté until onions are translucent.
Add minced garlic and cook for an additional minute until fragrant.
Stir in the flour to coat the vegetables, and cook for about 2 minutes.
Gradually whisk in chicken broth until there are no lumps. Allow it to come to a boil.
Reduce heat and simmer for 10 minutes, stirring occasionally.
Add the heavy cream, cooked chicken, and gnocchi. Let simmer for another 5 minutes until the gnocchi are tender.
Stir in the chopped spinach and let cook until wilted, about 3 minutes.
Season with thyme, salt, and pepper to taste before serving hot.