In a dutch oven over medium-high heat, warm you olive oil. When warmed, add onions and saute until softened. About 5 minutes. Add garlic and celery and cook an additional 5 minutes. Add carrots.
Slowly pour in a cup of chicken broth and scrape the bottom of your pan to remove the browned bits from the bottom of the pan. When incorporated into the chicken broth, add the remainder of the chicken broth.
Add cream cheese and stir together to incorporate it.
Add in your shredded chicken, herb bundle, saffron, salt and pepper. Stir.
If you are using leftover parmesan cheese rinds, add that now and dried tarragon.
Cover the pot and let simmer on medium-low for half an hour.
Add your gnocchi to the pot and stir. Continue to cook for another half hour. The gnocchi will release potato starch into the water to help thicken the broth a little bit as it cooks.
Remove from heat and eat. Or eat it the next day.
*If you are not using cheese rinds, add an additional 1/4 cup of cream cheese to the recipe for a creamier stew.
**Parmesan cheese rinds add a layer of umami-ness to this soup that can't be beat. I highly recommend as you buy and eat parmesan, to throw the rinds into the freezer and save for a soup-y day! They always add an unexpected "tang" to a recipe that can't be replicated.