Put the beef shanks and chopped onions a Dutch oven; cover with about 4 to 6 cups of water. Bring the water to a boil. Cover the pan, reduce the heat to low, and simmer the beef for 1 1/2 to 2 hours. Remove the meat from the bones, dice, and put back in the pot.
Sprinkle the stewing beef pieces with salt and pepper and toss with 2 tablespoons of flour.
Heat the olive oil in a large skillet over medium-high heat; add the stewing beef pieces and cook, stirring, until the outside of the beef has formed a browned crust. Add the browned beef to the pot with the beef shanks. Cover and cook over low heat for about 1 hour longer, or until beef is tender.
Add the rutabaga and carrots to the pot; cover and cook for 15 minutes. Add the potatoes; cover and cook for about 20 minutes, or until vegetables are tender. Add salt and pepper, to taste.
To thicken, if desired, stir the optional flour into the cold water until smooth. Stir about half of the flour mixture into the stew and continue to cook until thickened. Add more flour mixture if a thicker stew is desired.