Heat vegetable oil in a large pot or Dutch oven over medium-high heat. Brown the beef cubes in batches, then remove and set aside.
Add the chopped onions to the pot and cook until softened and translucent, about 5-7 minutes.
Stir in the minced garlic and cook for 1 minute more until fragrant.
Add the paprika, caraway seeds, salt, and pepper. Stir well to combine.
Return the browned beef to the pot. Pour in the beef broth and stir in the tomato paste.
Bring the mixture to a boil, then reduce heat to low, cover, and simmer for 1.5 hours, or until the beef is tender.
Add the cubed potatoes and sliced carrots to the pot. Stir to combine, cover, and continue to simmer for another 30-40 minutes, or until the vegetables are tender.
Serve hot, garnished with a dollop of sour cream if desired.
Notes
This goulash is even better the next day as the flavors meld together.