Heat the olive oil in a large pot over medium heat. Add the diced onion and cook for about 3-4 minutes until softened.
Stir in the minced garlic, sliced carrots, and diced celery. Continue to cook for an additional 5 minutes until the vegetables are tender.
Add the dried thyme, salt, and black pepper to the pot, stirring to combine.
Place the boneless chicken breasts into the pot, and pour in the chicken broth. Bring the mixture to a boil.
Reduce the heat to low and cover the pot. Simmer for about 15-20 minutes until the chicken is cooked through and tender.
Remove the chicken from the pot and shred it using two forks. Return the shredded chicken to the pot.
Stir in the heavy cream and bring back to a gentle simmer.
Add the gnocchi to the pot and cook according to package instructions, usually about 3-5 minutes until they float to the top.
Once the gnocchi is cooked, stir in the fresh spinach and let it wilt for about 2-3 minutes.
Taste and adjust seasoning if necessary. Serve hot, garnished with chopped parsley.