For the goulash: Preheat the oven to 250 degrees F.
Sprinkle the beef with 1/2 teaspoon salt and a few turns of pepper. Heat a Dutch oven over medium-high heat and coat with the oil. When the oil is shimmering, sear the beef all over in batches until deep brown, about 4 minutes per batch. Transfer the beef to a bowl and set aside.
Add the onions and cook, scraping up any meat bits from the bottom of the pan, about 3 minutes. Add the carrots, garlic and a pinch of salt and saute until the onions are translucent, about 5 minutes. Add the paprika, tomato paste and caraway and stir to combine; cook for 2 minutes. Add the beef back to the pan, then add the broth, chopped tomatoes, Worcestershire sauce and bay leaves and stir to combine. Bring to a boil, then reduce to a simmer. Cover, transfer to the oven and cook until the beef is tender and can be broken down with a spoon but still maintains its shape, about 2 hours.
For the bread dumplings: Meanwhile, whisk together the flour, nutmeg, 3/4 teaspoon salt and a few turns of pepper in a small bowl. Whisk together the milk and eggs in a large bowl. Add the bread cubes, cheese and scallions to the egg mixture and stir to combine. Mix in the flour mixture. Let the dumpling mixture sit for 15 minutes.
Bring a large pot of salted water to a boil. Using a 1/3-cup ice cream scoop, form firmly packed balls of the dumpling mixture. Add them to the pot and boil until cooked through, 15 to 20 minutes.
Spoon the goulash into bowls and add a dumpling or two to each. Top with chopped parsley or scallions if desired.