I don't know which experience you are seeking, but I have a recipe similar to it. I use fresh tomatoes, onions, carrots, anise (instead of celery), and chopped garlic. Saute them in butter in the large braising pot until there is hardly any liquid remaining.
Over high heat, brown lightly floured shanks on both sides. Remove them, deglaze the pan with 1/2 cup Marsala or Madeira, cook down a few minutes, add stock (chicken, veal, or otherwise), warm over and then pour it into the braising pot with vegetables. Add the shanks to the pot, turn up flame to boil the liquid, then turn it to low, cover tightly and let simmer for 2 hours.
When done, I run the sauce through a food mill (makes a great soup stock). And the gremolade (parsley, garlic, lemon rind).
I've forgotten something but have to go catch a plane...