Prepare the vegetables and chicken: Dice the onion, carrot, and celery, cut the chicken into bite-sized pieces, and mince the garlic.
Cook the vegetables: Heat a large pot over medium heat, add the olive oil, then cook the onion, carrot, and celery for about 5 minutes until they begin to soften.
Add the garlic and chicken: Stir in the garlic and cook for 30 seconds. Add the chicken, thyme, salt, and black pepper, then cook for 4 to 5 minutes until the outside of the chicken is no longer pink.
Pour in the broth: Add the chicken broth, stir well, bring to a gentle boil, then reduce the heat to medium-low and simmer for about 10 minutes.
Add the gnocchi: Stir in the gnocchi and cook according to the package directions, usually 3 to 5 minutes, until tender.
Add the cream: Lower the heat and slowly stir in the heavy cream. Warm gently for another 3 to 4 minutes without allowing the soup to boil hard.
Add the spinach: Stir in the fresh spinach and cook for 1 to 2 minutes until wilted.
Check the seasoning: Taste the soup and adjust the salt and pepper. Add a little extra chicken broth if it is thicker than you prefer.
Serve hot: Ladle the soup into bowls while the gnocchi is tender and finish with extra black pepper or fresh herbs if desired.