Place the quartered potatoes in an even layer in the bottom of a 5- to 5-1/2-quart slow-cooker pot. On top of the potatoes, first evenly layer the garlic, then the chopped onion, beef cubes, barley and cannellini beans.

Stir together the beef broth, water, ketchup, paprika, salt and black pepper in a small bowl until the mixture is well blended and smooth. Pour ketchup mixture over the beef mixture in the pot.

Cover the slow-cooker pot. Cook on high for 6 hours, or on low for 9 to 10 hours, until the meat, potatoes and barley are tender and the stew liquid is nicely thickened.

Cook the beef cubes in a large, heavy pot over medium-high heat until browned all over, about 10 minutes. Remove the beef cubes to a large plate. Reduce the heat to the medium. Add the onion and garlic to the drippings in the pot; saute until the vegetables are softened, 3 to 5 minutes. Return the browned beef cubes to the pot along with the potatoes, barley, drained beans, beef broth, water, ketchup, paprika, salt and black pepper. Cover the pot; bring to a boil. Lower the heat to medium-low; cook until the meat, potatoes and barley are tender, about 3 hours.