Step 1: Pat the beef stew meat dry with paper towels and season generously with salt and black pepper. Heat 1 tablespoon of olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Brown the beef in batches, ensuring not to overcrowd the pot. This creates a beautiful crust and locks in flavor. Remove browned beef to a plate and set aside.
Step 2: Reduce heat to medium. Add the remaining 1 tablespoon of olive oil to the pot. Add the chopped onions and cook until softened and translucent, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant. Stir in the sweet paprika and, if using, the tomato paste. Cook for 1 minute, stirring constantly, allowing the paprika to bloom and release its flavor.
Step 3: Deglaze the pot by pouring in the beef broth. Scrape up any browned bits from the bottom of the pot with a wooden spoon – these are packed with flavor! Return the browned beef to the pot. Stir in the crushed tomatoes, bay leaves, and caraway seeds (if using). Bring the mixture to a gentle simmer.
Step 4: Cover the pot and reduce the heat to low. Let the goulash simmer gently for 2 to 2.5 hours, or until the beef is fork-tender. Stir occasionally to prevent sticking. The longer it simmers, the more tender the beef and the richer the flavors will become.
Step 5: If using, add the chopped bell peppers about 30-45 minutes before the end of the cooking time, so they retain a bit of texture. For a thicker sauce, you can remove the lid for the last 30 minutes of simmering.
Step 6: Once the beef is tender, remove the bay leaves. Taste and adjust seasoning with salt and pepper as needed. A pinch of sugar can balance the acidity of the tomatoes if desired. Serve hot, garnished with fresh parsley and a dollop of sour cream or Greek yogurt, if desired.