Heat olive oil in a large Dutch oven over high heat. Pat beef dry and season with salt and pepper. Brown in batches, searing on all sides until deeply golden, 2 to 3 minutes per side. Transfer browned beef to a plate.
2 tablespoons olive oil, 2 pounds stewing beef
Reduce heat to medium-high. Add onions, carrots, and celery to the same pot. Sauté for 5-6 minutes until lightly browned.
2 yellow onions, 1 large carrot, 1 celery stalk
Add tomato paste. Stir constantly for 1 minute. Then add paprika, marjoram, and hot paprika or cayenne if using. Stir for 30 seconds.
2 tablespoons tomato paste, 2 tablespoons sweet paprika, 1 teaspoon dried marjoram, 1 teaspoon hot paprika
Pour in red wine and beef broth. Scrape the bottom of the pot with a spatula to release any browned bits. Bring to a simmer.
1 cup red wine, 2 cups beef broth
Return beef to the pot along with any resting juices. Add bay leaves. Reduce heat to low. Simmer covered for about 2 hours, stirring occasionally, until the meat is fork-tender and the sauce has thickened.
2 bay leaves
If adding potatoes or bell peppers, add them 30 minutes before the cook time ends.
Remove bay leaves. Taste and adjust salt and pepper.
1 teaspoon salt, ¼ teaspoon ground black pepper
To thicken: Combine water and cornstarch in a small bowl and add it to the goulash. Bring to a simmer while stirring constantly until thickened.
2 tablespoons water, 2 tablespoons cornstarch
Serve over bread or potato dumplings, spaetzle, or with crusty bread.