Start by warming olive oil in a large pot over medium heat. Add the onions, carrots, celery, and garlic. Sauté everything until the onions turn soft and translucent. This builds the flavor base.
Drop the diced chicken into the pot, then pour in the chicken broth. Add thyme, salt, and pepper. Bring the pot to a gentle boil, then stir in the gnocchi so it cooks evenly and absorbs the broth.
Once the gnocchi softens, lower the heat and let the soup simmer for about 10 minutes. Pour in the half and half and mix in the chopped spinach. Cook just until the spinach wilts, then taste and adjust the seasoning.