Add the beef stew to a large saucepan and heat over medium heat until warm. Shred the meat using two forks. Add the wine to the stew and bring to a simmer, then simmer 10 to 15 minutes.
Generously salt the boiling water. Add the pasta and cook to al dente, about 2 minutes less than the package instructions. Drain, reserving about 1 cup pasta water. Place the pasta pack in the pot.
Add the ragu to the cooked pasta and stir to combine. If the sauce is too thick, add some pasta water to thin it out. Finish with the olives, fresh tomatoes, Parmesan and extra-virgin olive oil. Top with the whole basil leaves. Serve immediately.