Finely chop the onions, garlic, tomato, and bell pepper. Cut the beef into medium-sized cubes.
Heat the oil in a large pot or Dutch oven over medium heat. Sauté the onions until translucent. Add the garlic and cook for another minute until fragrant, then stir in the Hungarian sweet paprika.
Add the beef to the pot and sear until browned on all sides. Stir in the diced tomato and bell pepper, then season with salt and pepper to taste.
Pour in enough water to cover the beef. Bring to a simmer, then cover and cook over low heat for about 2 hours, or until the beef is tender.
While the stew is cooking, prepare the dumplings: In a bowl, combine the flour, eggs, water, and a pinch of salt. Mix until you have a smooth, slightly sticky dough.
Bring a large pot of salted water to a boil. Using a dumpling maker or a small spoon, drop small portions of the dough into the boiling water. Cook until the dumplings float to the surface (about 2-3 minutes), then drain.
Serve the beef stew hot with the freshly cooked dumplings. Garnish with fresh parsley, if desired.
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