In a large Dutch oven or heavy-bottomed pot, heat the vegetable oil over medium-high heat. Brown the beef in batches, then remove and set aside.
Add the chopped onions to the pot and cook until softened and translucent, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant.
Stir in the Hungarian sweet paprika, crushed caraway seeds, and dried marjoram. Cook for 1 minute, stirring constantly, until fragrant. Be careful not to burn the paprika.
Return the browned beef to the pot. Add the beef broth, diced tomatoes (undrained), and tomato paste. Stir to combine.
Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for at least 1.5 hours, or until the beef is tender.
Add the cubed potatoes and sliced carrots to the pot. Stir, cover, and continue to simmer for another 30-45 minutes, or until the vegetables are tender.
Season the goulash with salt and black pepper to taste.
Serve hot, optionally with a dollop of sour cream.
Notes
This Hungarian Goulash is best served with crusty bread or noodles.