Preheat Oven: Preheat the oven to 180°C/350°F, or 160°C fan-forced.
Season Beef: Place the beef in a bowl and toss it with half of the salt and all of the black pepper until evenly seasoned.
Cook Onion: Heat the olive oil and melt the butter in a large oven-proof Dutch oven over high heat. Add the onions and cook for 6 minutes, stirring as needed, until the edges become lightly golden. Cook Beef: Add the seasoned beef to the pot and stir for about 2 minutes, until the exterior changes from red to brown. The beef does not need to develop a deep golden crust. Add Vegetables: Add the minced garlic, bell peppers, and tomatoes. Stir and cook for 3 minutes, allowing the tomatoes to break down substantially.
Add Paprika and Spices: Stir in the Hungarian-style paprika, optional caraway seeds, and bay leaf. Cook while stirring for 30 seconds.
Add Stock and Begin Slow Cooking: Pour in the beef stock and stir well. Bring the liquid to a simmer, then cover the Dutch oven with its lid and transfer it to the preheated oven. Cook for 1 1/2 hours. Add Carrots and Potatoes: Carefully remove the pot from the oven.The beef should be quite tender but not yet completely fall-apart. Stir in the carrots and potatoes, cover again, and return the pot to the oven for 30 minutes. Check Beef Tenderness: After 30 minutes, check that the beef is fall-apart tender. If it is not yet tender enough, return the covered pot to the oven and continue cooking in additional 10-minute intervals until the desired tenderness is reached.
Serve: Ladle the Hungarian beef goulash into bowls and sprinkle with finely chopped parsley, if using. Serve as is or with bread for dipping into the flavorful broth.