Heat vegetable oil in a large Dutch oven or heavy-bottomed pot over medium heat. Add the sliced onions and cook until they become translucent and begin to caramelize, about 5-7 minutes. Remove onions with a slotted spoon and set aside.

Working in batches, add the beef cubes to the pot and brown on all sides, about 3-4 minutes per batch. Don't overcrowd the pot or the meat will steam instead of brown.

Return the onions and all browned beef to the pot. Reduce heat to low and add the paprika, stirring constantly for 30 seconds to toast the spice but prevent it from burning.

Add caraway seeds and minced garlic, stirring for another minute until fragrant.

Stir in the tomato paste and mix well to coat the meat and onions.

Pour in the beef broth and water, then add bay leaves, salt, and pepper. Bring to a gentle simmer.

Cover and reduce heat to low. Let the goulash simmer for 1 hour and 15 minutes, occasionally stirring and checking that there's enough liquid.

Add the bell peppers, carrots, and potatoes (if using). Continue simmering for 30-40 minutes more, until the meat is fork-tender and the vegetables are cooked through.

If you prefer a thicker stew, stir in the flour and water mixture during the last 5 minutes of cooking.

Remove bay leaves, taste, and adjust seasoning if needed.

Serve hot in bowls, garnished with fresh parsley and a dollop of sour cream.