Cook the meat: Heat a Dutch oven over high heat and add the canola oil. Season the pieces of beef on all sides with salt and pepper. When the oil begins to smoke lightly, use a pair of metal tongs to arrange the beef in a single layer in the hot oil, making sure not to crowd the pan (you might need to cook the beef in batches). Brown the meat on all sides. When brown, add onions and steam over the beef, 2 to 3 minutes. Add the wine and vinegar and cook until all of the liquid evaporates, 10 to 15 minutes. Add stock and mustard and continue to simmer about 8 to 10 minutes more. Meanwhile, in a medium skillet, add parsnips and enough water just to cover. Add 2 tablespoons butter, brown sugar, and bay leaves and simmer until parsnips are slightly tender, 4 to 5 minutes. Drain, discard bay leaves, and set parsnips aside. In the same pan, add carrots and enough water just to cover. Add remaining 2 tablespoons butter and the olive oil. Simmer until slightly tender, 4 to 5 minutes. Drain and set aside.
Cook and finish the stew: Add the parsnips and carrots to the beef. Cover and place in the center of the oven. Cook until the meat is tender when pierced with the tip of a knife, 1 to 1 1/2 hours. Remove the stew from the oven and use a large spoon to skim any excess fat or impurities that form on the surface. Taste for seasoning. Allow it to "rest" for 15 minutes before serving. Stir in the peas, parsley and chives.