In a heavy 4 quart dutch oven, heat oil over medium heat. Add beef and saute, turning cubes, until lightly browned on all sides. With slotted spoon, transfer cubes to plate. Add celery, carrots, and onion. Cook until barely softened, scraping any fragments that might be stuck to bottom of pan, about 1 minute.
If vegetables start to stick to pan, add 2 tablespoons broth. Return beef to pan and add wine. Turn heat to high and cook, stirring frequently, until wine is reduced to 2 tablespoons, about 4 minutes. Stir in lemon juice, broth, basil, salt, and pepper. Turn heat to low and cook, covered, stirring frequently, until meat is extremely tender when pierced with tip of a knife, about 1 1/2 hours.
As soon as meat is cooked, uncover pan, turn heat to medium high, and cook, stirring frequently, until sauce is slightly thickened, about 10 minutes. Transfer to shallow bowl, garnish with parsley, and serve. (Stew can be made up to 3 hours before serving and reheated, covered, over low heat.)