Step 1: Pat the beef chunks dry with paper towels. Season generously with salt and pepper.
Step 2: Heat 1 tablespoon of olive oil in a large, heavy-bottomed skillet or Dutch oven over medium-high heat. Sear the beef in batches until deeply browned on all sides. Remove beef and set aside.
Step 3: Add the remaining 1 tablespoon of olive oil to the same skillet (add a little more if needed). Add the finely diced onion, carrots, and celery. Cook over medium heat, stirring occasionally, until softened, about 8-10 minutes.
Step 4: Add the minced garlic and tomato paste to the skillet. Cook for another 2-3 minutes, stirring constantly, until the tomato paste darkens slightly and becomes fragrant.
Step 5: Pour in the red wine (if using) and scrape the bottom of the skillet with a wooden spoon to loosen any browned bits. Let it simmer for 2-3 minutes until the liquid reduces by about half.
Step 6: Transfer the sautéed vegetables and deglazing liquid to your slow cooker. Add the seared beef chunks, crushed tomatoes, diced tomatoes, beef broth, bay leaves, dried oregano, and dried thyme. Stir gently to combine.
Step 7: Season with a good pinch of salt and freshly ground black pepper.
Step 8: Cover your slow cooker and cook on low for 8-10 hours, or on high for 4-5 hours, until the beef is incredibly tender and easily shreds with a fork.
Step 9: Once cooked, carefully remove the beef chunks from the slow cooker and place them on a cutting board. Using two forks, shred the beef into bite-sized pieces. Discard any large pieces of fat or gristle.
Step 10: Return the shredded beef to the slow cooker and stir it into the rich tomato sauce.
Step 11: For an even thicker, more concentrated sauce (optional), remove 1-2 cups of the liquid from the slow cooker and simmer it in a saucepan on the stovetop over medium-high heat until it reduces to your desired consistency. Then, stir it back into the slow cooker beef ragu.
Step 12: Taste the slow cooker beef ragu and adjust seasonings as needed. Remove the bay leaves before serving. Ladle over your favorite pasta, polenta, or mashed potatoes. Garnish with fresh herbs and Parmesan cheese.