Heat the pork lard or vegetable oil in a large Dutch oven over medium-high heat. Add the chopped yellow onions and cook for 8 to 10 minutes until softened and lightly browned.
Add the cubed beef chuck roast to the pot. Cook for 5 to 7 minutes until the meat is browned on all sides, then stir in the minced garlic for 1 minute.
Remove the pot from the heat completely. Stir in the sweet Hungarian paprika and crushed caraway seeds, tossing until the meat and onions are fully coated.
Return the pot to the stove over medium heat. Add the diced Roma tomatoes, chopped mild chili peppers, beef broth, salt, and black pepper. Bring the liquid to a boil.
Reduce the heat to low, cover the pot tightly, and simmer for 1 hour and 30 minutes, or until the beef is mostly tender.
Stir in the sliced carrots and cubed Yukon gold potatoes. Cover and continue to simmer for an additional 30 to 40 minutes, until the vegetables are fork-tender and the beef is completely soft.
Taste the broth and adjust the seasoning if necessary. Ladle the hot stew into bowls, garnish with chopped fresh parsley, and serve immediately.