Melt oil and butter In a large Dutch oven over medium.
Add onions, cooking 5 minutes.
Add shallots, garlic, celery, and carrots.
Add just a touch of salt and cook an additional 5 minutes.
Add the sherry and broth.
Bring up to a boil. I added 2 T. kosher salt. (We like salt so you may want to try less-can always add more later.)
Add chicken pieces, dill and parmesan rind.
Cover and lower to a simmer for 60-90 mins.
Remove chicken and shred, discarding bones. Remove rind.
Taste for salt!
Optional: Stir in cream