1. In 12-inch skillet over medium heat, in hot salad oil, cook onion until tender, stirring occasionally. With slotted spoon, remove onion to large bowl; add ground beef, bread crumbs, egg, 1/4 cup water, 3/4 teaspoon salt, and 1/4 tea spoon basil; mix well. Shape meat mixture into 1 1/2 inch meatballs.
2. In drippings in skillet, over medium-high heat, cook meatballs until browned, removing meatballs to plate as they brown and adding oil if necessary. In drippings, cook potatoes and carrots until browned, stirring occasionally.
3. Return meatballs to skillet; add Brussels sprouts, bouillon, 2 cups water, 1 teaspoon salt, and 1/4 teaspoon basil; over high heat, heat to boiling. Reduce heat to low; cover; simmer 20 minutes or until vegetables are tender.
4. In cup, stir flour with 1/4 cup water; stir mixture into simmering liquid in skillet; cook, stirring, until mixture thickens slightly.