Peel and chop the vegetables into 1 inch chunks.
Heat the vegetable oil in a large Dutch oven over medium high heat.
Pat the shanks dry with a paper towel and sprinkle with salt and pepper. Toss the shanks with the flour in a bag to coat. Shake off any excess flour and reserve remaining flour.
Brown the lamb shanks well on all sides (3-4 minutes per side). Work in batches so shanks are in a single layer while browning. Transfer browned shanks to a platter and set aside.
Add the onions to the pan and cook about 7 minutes. Scrape up any browned bits from the bottom of the Dutch oven. Sprinkle remaining flour over the onions and stir to mix. Cook about 2 minutes.
Return the shanks and any juices to the Dutch oven. Add the beef stock and the Guinness.
Bring to a boil, then reduce heat and simmer covered about 1 hour.
Add the carrots, parsnips and rutabaga and simmer uncovered another 40 minutes until vegetables are tender.
Add the prunes and simmer another 20 minutes. If you want a thicker sauce dissolve 2 Tbsps flour in 2 Tbsps water and add to the stew at this point, stirring well.
You can easily make this a day ahead and refrigerate. Reheat gently over medium low heat and serve.