In a large stock pot, heat the vegetable oil over medium-high heat.
Add the beef stew meat to the pot and cook until browned on all sides, about 5-7 minutes. Remove the meat from the pot and set aside.
In the same pot, add the diced onions and cook until softened and lightly caramelized, about 5-7 minutes.
Add the minced garlic, Hungarian sweet paprika, caraway seeds, salt, and black pepper to the onions. Stir to combine and cook for 1-2 minutes until fragrant.
Stir in the tomato paste and cook for an additional 1-2 minutes.
Pour in the beef broth, scraping the bottom of the pot to deglaze and release any browned bits.
Return the browned beef to the pot and add the sliced carrots, cubed potatoes, and bay leaves.
Bring the mixture to a boil, then reduce the heat to low, cover the pot, and simmer for 1 1/2 to 2 hours, or until the beef is tender and the vegetables are cooked through.
Remove the bay leaves and discard.
Serve hot, garnished with chopped fresh parsley, if desired.
Notes
For a thicker goulash, you can remove 1/2 cup of the cooking liquid and mix it with 2 tablespoons of flour to make a slurry. Stir this mixture back into the pot and simmer for an additional 5-10 minutes,or until the goulash has thickened to your desired consistency.Refrigerate any leftovers in an airtight container for up to 5 days.