1. Heat oil in 12-inch skillet over medium-high heat until shimmering. Add onions, carrots, and celery and cook until vegetables are softened and lightly browned, 8 to 10 minutes. Stir in tomato paste and garlic and cook until fragrant, about 1 minute. Stir in wine, scraping up any browned bits, and simmer until thickened, about 6 minutes; transfer to slow cooker.
2. Stir in diced tomatoes, tomato puree, and bay leaves. Season beef with salt and pepper and nestle into slow cooker. Cover and cook until beef is tender, 9 to 10 hours on low or 6 to 7 hours on high.
3. Discard bay leaves. Using large spoon, skim excess fat from surface of sauce. Break beef into bite-size pieces with tongs. Stir in parsley and season with salt and pepper to taste. Serve.