Heat the olive oil in a large pot over medium heat. Add the beef and cook until browned on all sides. Remove the beef and set aside.
In the same pot, add the onions and cook until softened. Add the garlic, paprika, and caraway seeds, and cook for another minute.
Stir in the tomato paste and cook for another minute. Return the beef to the pot and pour in the beef broth. Bring to a boil, then reduce the heat and simmer for 1.5 hours.
Add the carrots and potatoes to the pot. Season with salt and pepper. Continue to simmer for another 30 minutes, or until the vegetables are tender.
Adjust seasoning if necessary. Serve hot.
Notes:
For a richer flavor, let the goulash sit overnight in the fridge and reheat before serving.