Spread the onion in the bottom of a 5 to 6-quart slow cooker. Top with the carrots. Toss the beef with 1/4 teaspoon salt and 1/4 teaspoon pepper and spread over the vegetables. Sprinkle with the garlic and add the basil sprig.
Whisk together the wine, if using, tomato paste, flour, tomatoes and 1/2 teaspoon salt until smooth and pour over the beef. Cover and cook on high for 5 hours or on low for 7 to 8 hours.
When the sauce is almost done, bring a medium pot of water to a boil and cook the pasta according to package directions. Drain.
Remove the basil sprig from the sauce and stir in 1/4 teaspoon salt. Gently break up the meat cubes using a fork by pulling them to the side of the slow cooker (you are not trying to shred the meat, but break it down into smaller pieces). Season with additional salt and pepper. Stir in the torn basil and serve over the pasta.
Per serving: Calories: 394; Total Fat: 6 grams; Saturated Fat: 2 grams; Protein: 31 grams; Total carbohydrates: 54 grams; Sugar: 8 grams; Fiber: 10 grams; Cholesterol: 62 milligrams; Sodium: 218 milligrams