Place corned beef in a 6-quart Dutch oven or heavy pot and pour in enough water to cover beef by 2 inches. Bring water to a boil, skimming the liquid occasionally to remove fat from top. Reduce heat to medium-low, cover Dutch oven with a lid, and simmer for 2 hours.
Arrange cabbage, potatoes, onions, and carrots around beef and return liquid to a boil. Lower heat to medium-low, cover Dutch oven, and simmer until vegetables are tender, about 40 minutes. Transfer beef to a serving platter, reserving 1 1/2 cups cooking liquid. Surround meat with the vegetables.
Melt butter in a small saucepan over medium heat. Whisk flour into melted butter until dissolved and bubbling, about 1 minute. Add reserved cooking liquid and vinegar to butter-flour mixture; cook, stirring frequently, until sauce is slightly thickened, about 4 minutes. Remove saucepan from heat and whisk sour cream and mustard into sauce. Serve sauce alongside corned beef and vegetables.