Heat the vegetable oil in a heavy-bottomed stock pot over medium-heat. Heat the beef cubes in the oil until browned, about 4 minutes. Add the onions and cook until wilted, about another 3 minutes.
Add 3 cups of water, sherry, soy sauce, ginger, sugar, potatoes, and carrots and beef base. Bring the soup to a simmer. Stir in the peppers and broccoli. Simmer until the beef and vegetables are just cooked, about 15 minutes. Stir in the Tabasco sauce.
Combine ¼ cup of water with the corn starch in a small bowl to make a slurry. Stir into the soup and allow to thicken, stirring frequently, about another 5 minutes.