Heat the vegetable oil in a Dutch oven or large pot over medium heat. Add the chopped onions and cook until softened, about 5 minutes.

Add the minced garlic to the pot and cook for an additional 1-2 minutes, until fragrant.

Increase the heat to medium-high and add the beef chunks to the pot. Brown the meat on all sides, stirring occasionally, for about 5-7 minutes.

Sprinkle the sweet paprika, smoked paprika (if using), caraway seeds, dried thyme, and bay leaves over the meat. Stir well to coat the meat evenly with the spices.

Add the tomato paste to the pot and cook, stirring constantly, for 1-2 minutes to develop its flavor.

Pour in the beef broth and diced tomatoes with their juices. Season with salt and pepper to taste.

Bring the mixture to a boil, then reduce the heat to low and cover the pot with a lid. Simmer the goulash gently for 1.5 to 2 hours, stirring occasionally, until the beef is tender and the flavors have melded together.

Once the goulash is cooked to your desired consistency, taste and adjust the seasoning if necessary.

Remove the bay leaves from the pot before serving.

Garnish the goulash with chopped fresh parsley, if desired, and serve hot with your choice of accompaniment, such as cooked pasta, mashed potatoes, or crusty bread.

Enjoy your hearty and flavorful homemade goulash!