Heat the vegetable oil in a large stock pot or Dutch oven over medium-high heat.
Add the beef stew meat in a single layer and brown on all sides, about 5–7 minutes. Work in batches if needed. Transfer the browned beef to a plate.
Add the onions to the same pot and cook for 5–7 minutes, stirring occasionally, until softened and lightly browned.
Stir in the garlic, paprika, caraway seeds, salt, and black pepper. Cook for 1 minute until fragrant.
Add the tomato paste and cook for 1–2 minutes, stirring constantly.
Pour in the beef broth, scraping the bottom of the pot to loosen any browned bits.
Return the beef to the pot. Add the carrots, potatoes, and bay leaves, then stir to combine.
Bring the stew to a boil. Reduce the heat to low, cover, and simmer for 1½–2 hours, stirring occasionally, until the beef is fork-tender and the vegetables are cooked through.
Remove and discard the bay leaves. Taste and adjust the seasoning with additional salt and pepper if needed.
Ladle into bowls and garnish with fresh parsley before serving, 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.