Step 1: Pat the beef cubes dry with paper towels and season generously with salt and pepper. Heat the oil in a large Dutch oven over medium-high heat.
Step 2: Brown the beef in batches, ensuring not to crowd the pan, until a deep crust forms on all sides. Remove the meat and set aside.
Step 3: In the same pot, add the chopped onions. Reduce heat to medium and cook for 10-15 minutes, stirring occasionally, until the onions are soft and golden brown.
Step 4: Remove the pot from the heat briefly. Stir in the Hungarian paprika, caraway seeds, and minced garlic, allowing them to bloom in the residual heat for about 30 seconds.
Step 5: Add the tomato paste and stir to combine. Return the pot to the heat and deglaze with a splash of beef broth, scraping the bottom of the pan to release the fond.
Step 6: Return the browned beef and any accumulated juices to the pot. Pour in the remaining beef broth until the meat is just covered.
Step 7: Bring the mixture to a boil, then immediately reduce the heat to low. Cover with a tight-fitting lid and simmer for 2 hours.
Step 8: If using peppers and potatoes, add them to the pot after 2 hours. Continue simmering for another 45-60 minutes until the meat is fork-tender and the sauce has thickened.
Step 9: Adjust seasoning with salt and pepper. Let the Goulash recipe rest for 10 minutes before serving over egg noodles or with crusty bread.