Preheat a heavy-bottomed pot over medium-low heat. Add the butter. Once melted, add the carrots, celery, and onion. Increase the heat to medium and cook for 5 to 6 minutes, or until slightly softened. If the onion starts to brown, reduce the heat a bit.
Add the chicken stock and ½ teaspoon salt. Place the lid on the pot. Increase the heat and bring the soup to a boil. Reduce the heat to gently boil the stock for 8 to 9 minutes to soften the vegetables, stirring occasionally.
Remove the lid and reduce the heat to medium. Add the cream when the liquid is no longer boiling hard (gently bubbling or simmering is fine—reduce the heat if you need to). Stir well to combine and allow the cream to heat in the soup until steamy.
Add the baby spinach. Once it has wilted into the hot soup, add the chicken, gnocchi, and black pepper. Stir to combine then raise the heat a bit and simmer for 5 minutes.
Stir in the Parmesan cheese and lemon zest. Taste the soup to see if more salt and pepper is needed. Adjust the seasoning to your liking. Serve the soup hot, topped with a sprinkle of grated Parmesan cheese.
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Notes
Three cups of chicken is approximately the meat of one rotisserie chicken.
Cut the carrots, celery, and onion to roughly the same size so they cook evenly in the early steps.
Add the spinach in handfuls if it doesn’t all fit at once; it wilts quickly as it hits the hot broth.
Don't omit the lemon zest if you can help it. The soup is delicious without it, but the lemon zest adds a bright note that takes it to the next level.
Storage
Store your soup in airtight containers with tight-fitting lids in the refrigerator for up to four days.
I haven't tried freezing this soup because we usually eat it too quickly.