Place beef chunks in a large bowl. Sprinkle liberally with kosher salt and freshly ground pepper.
Toss with the flour.
Heat a heavy Dutch oven over medium high heat and add 1 tablespoon of the olive oil. Swirl to coat the bottom of the pan. Place beef chunks in a single layer and brown on two sides. You will probably need to do this in batches. Do not crowd the meat or it will boil instead of brown. Remove browned beef chunks to a bowl.
Reduce heat to medium-low. To the drippings in the Dutch oven, add the remaining 2 tablespoons of olive oil, sweet onion rings, mushrooms, and garlic. Toss to coat with the olive oil. Cover tightly and sweat the vegetables, stirring occasionally, until onions are limp but not browned and mushrooms are releasing their liquid, about 10 minutes.
Add red wine to the vegetables and cook 2 minutes. Add beef broth and paprika. Return beef to the pan. Stir until well-combined. Cover tightly, reduce heat, and simmer on low heat for 1-1/2 to 2 hours, stirring occasionally, until beef is fork-tender.
Remove Dutch oven from heat and wait for boiling to subside. Taste and add additional salt if necessary. Stir in sour cream until completely incorporated into the gravy.
Serve Hungarian gulash over hot buttered noodles with chopped parsley.
Note: The amount of paprika is correct. Please do use it all. If you cannot use the wine, use an equal amount of additional beef broth. The goulash may be frozen, before the addition of the sour cream. Reheat and add the sour cream just before serving.