Begin by preparing the beef for the cooking process. Take a large bowl, and put in the beef chunks. Then add in salt and freshly ground black pepper to taste, along with the flour. Toss it all together, until the beef is completely coated with the flour and seasonings.
Next, place a heavy Dutch oven on the stove over medium heat, and drizzle in a tablespoon of olive oil. Move the oil about, until it coats the bottom of the pan entirely and evenly. Now, start browning the beef. It is essential not to crowd the pan, otherwise the beef won’t brown, so do not throw all the beef in at once – rather, do this in batches. Place a single layer of chunks in the oil, brown them from all sides, remove and put in a bowl, and then brown another batch in a similar fashion. Repeat, until all the beef has been browned.
Once this is done, turn the heat down to low. The bottom of the pan will be coated with beef drippings and juices, which you will now use to flavour your stew. Add the sweet onion rings, mushrooms, and garlic to the Dutch oven, along with the remaining 2 tablespoons of oil. Stir, to coat the vegetables with the oil, and then cover the pot and sweat the vegetables for around 10 minutes, until the onions and mushrooms become soft.
Next, pour in the red wine, and cook for around 2 minutes, to make sure all the alcohol burns off. Scrape the bottom of the pan as the wine and vegetables cook, to release any browned, flavourful bits stuck to the pan. Then add in the beef broth, roasted red peppers, and paprika, along with the browned beef chunks. Stir everything together until it is all combined, then cover the pan, reduce the heat, and allow the stew to cook for 1-1/2 to 2 hours on low heat.
Once the beef becomes tender, you will know the goulash is done. Take the Dutch oven off the heat, and wait for the stew to stop bubbling. Then, stir in the sour cream, taste to check for seasonings, and finally, serve over hot buttered noodles, with a generous sprinkling of fresh chopped parsley and an additional dollop of sour cream.