Step 1: Pat the beef cubes thoroughly dry with paper towels. Season generously with 1 teaspoon salt and 1/2 teaspoon black pepper.
Step 2: Heat a large Dutch oven or heavy-bottomed pot over medium-high heat. Add 1-2 tablespoons of olive oil. Once shimmering, add the beef in batches, ensuring not to overcrowd the pot. Sear on all sides until deep golden brown. Remove the browned beef to a separate plate and set aside.
Step 3: Reduce heat to medium. Add the chopped onions to the pot (add more oil if needed) and a pinch of salt. Cook slowly, stirring occasionally, for 10-15 minutes until the onions are very soft and translucent, almost melting and lightly caramelized.
Step 4: Stir in the minced garlic and cook for another minute until fragrant, being careful not to burn it.
Step 5: Remove the pot from the heat. Stir in the sweet Hungarian paprika, caraway seeds, dried marjoram, and cayenne pepper (if using) until fragrant, about 30 seconds, using the residual heat of the pot to bloom the spices.
Step 6: Return the pot to medium heat. Deglaze the pot with 1/2 cup of beef broth, scraping up any browned bits from the bottom of the pot with a wooden spoon.
Step 7: Stir in the tomato paste and cook for 2-3 minutes, stirring constantly, until it darkens in color.
Step 8: Return the browned beef and any accumulated juices to the pot. Add the diced bell peppers and pour in the remaining 3.5 cups of beef broth. The liquid should just about cover the meat and vegetables.
Step 9: Bring the mixture to a gentle simmer. Add the bay leaves. Cover the pot tightly and reduce the heat to low.
Step 10: Simmer gently for at least 2.5 to 3 hours, or until the beef is fork-tender. Stir occasionally to prevent sticking and ensure even cooking.
Step 11: Once the beef is tender, remove the bay leaves. Taste the goulash and adjust seasoning with additional salt and pepper as needed. If the sauce is too thin, uncover and simmer for an extra 15-30 minutes to reduce. If too thick, add a little more beef broth or water.
Step 12: Serve hot, garnished with fresh parsley or chives, and a dollop of sour cream or crème fraîche if desired. Excellent with egg noodles, mashed potatoes, or crusty bread.