Pat the beef chuck cubes completely dry with paper towels — this is essential for a good sear. Season generously on all sides with 1 teaspoon of the kosher salt and the black pepper.

Heat the oil in a large Dutch oven or heavy-bottomed pot over medium-high heat until shimmering and very hot. Working in 2–3 batches, add the beef in a single layer without crowding the pan. Sear undisturbed for 3–4 minutes per side until deeply browned. Transfer to a plate and repeat with remaining beef. Set aside.

Reduce heat to medium. Add a small drizzle of oil if the pan is dry, then add the diced onions. Cook, stirring occasionally, for 10–12 minutes until the onions are very soft, golden, and beginning to turn translucent. Do not rush this step — softened, caramelized onions are the flavor foundation of the stew.

Add the minced garlic and diced bell peppers. Cook for 2 minutes, stirring frequently, until fragrant and slightly softened.

Push the vegetables to the sides of the pot and add the sweet paprika (and hot paprika if using) to the center of the pan. Let it bloom in the residual heat and oil for 45–60 seconds, stirring constantly, until fragrant and darkened slightly. Be careful not to burn it. Then stir the paprika together with the vegetables.

Add the tomato paste and stir it into the vegetable mixture. Cook for 1–2 minutes until the paste darkens slightly and loses its raw smell.

Return the seared beef and any accumulated juices on the plate back to the pot. Add the diced tomatoes, beef broth, caraway seeds (if using), and remaining half teaspoon of salt. Stir everything together, scraping up any browned bits from the bottom of the pot.

Bring the liquid to a gentle boil, then reduce heat to low. Cover the pot with a lid slightly ajar and simmer for 60 minutes, stirring occasionally.

After 60 minutes, add the diced potatoes. Continue to simmer, partially covered, for another 30–35 minutes until the potatoes are tender and the beef is completely fork-tender and nearly falling apart.

Taste and adjust seasoning with additional salt and pepper as needed. Stir in the lemon juice or red wine vinegar — this brightens all the flavors and balances the richness.

If using sour cream, remove the pot from heat and stir in the sour cream until fully incorporated. Do not boil the stew after adding sour cream or it may curdle.

Ladle the goulash into bowls over cooked egg noodles or mashed potatoes. Garnish generously with fresh chopped parsley and serve immediately. Offer extra sour cream on the side if desired.