Preheat the Oven. Place the oven rack in the center of the oven and preheat to 325°.
Sauté Onions. Add 2 tablespoons olive oil to a heavy pot or Dutch oven and heat over medium heat. Add the chopped onions and half a teaspoon of kosher salt. Cook for about 15-20 minutes, stirring occasionally until the onions are very tender and golden brown.
Brown the Beef. Transfer the cooked onions to a separate dish and set aside. Season the beef chuck roast or stew beef with the remaining salt and black pepper before transferring it to the Dutch Oven. Cook over medium-high heat for approximately 5-10 minutes until browned on all sides.
Combine Ingredients. Stir in the reserved onions along with chopped green pepper, diced tomato, minced garlic, Hungarian paprika, dried marjoram, caraway seed, tomato paste, beef broth, apple vinegar, and bay leaf into the pot. Heat this mixture until it reaches boiling.
Braise in Oven. Once boiling, place the lid on the pot slightly askew so steam can escape naturally during cooking; transfer it to the preheated oven and allow it to cook for about an hour and a half until the beef becomes tender.
Finish and Serve. After removing from the oven, garnish your goulash with freshly chopped parsley before serving alongside spaetzle, buttered noodles, or potatoes.