Buttered egg noodles or whole wheat bread, for serving
Heat the oil in a large Dutch oven over medium-high heat. Add the onions and saute until tender, about 6 minutes. Add the garlic and some salt and pepper and saute until fragrant, about 1 minute. Lower the heat (so the paprika won't burn and give a bitter taste or grainy texture in the final dish) and stir in the paprika.
Sprinkle the beef on all sides with salt and pepper. Return the pot to medium-high heat, and add the beef cubes to the pot, turning to cover the beef with the paprika-onion mixture, and cook until browned, about 6 minutes. Add 2 cups cold water, cover with a lid, reduce the heat to medium and stew for 45 minutes.
Remove the lid and add the potatoes, carrots, tomatoes and green peppers, cover and stew until the beef is tender, about 30 minutes more, stirring on occasion. Adjust to taste with salt and pepper.
Serve with buttered noodles or with whole grain bread to sop up the juices.