Step 1: Heat olive oil in a large skillet over medium-high heat. Add ground beef and cook, breaking it apart with a spoon, until browned. Drain any excess fat.
Step 2: Add chopped onion and minced garlic to the skillet with the browned beef. Cook until the onion is softened and translucent, about 5-7 minutes.
Step 3: In a medium bowl, whisk together the crushed tomatoes, diced tomatoes (with their juice), beef broth, brown sugar, Worcestershire sauce, dried oregano, salt, and black pepper. Stir well to combine.
Step 4: Place about one-third of the chopped cabbage at the bottom of a 6-quart or larger slow cooker, spreading it evenly.
Step 5: Spread half of the browned ground beef and onion mixture over the cabbage layer.
Step 6: Ladle about one-third of the prepared tomato sauce over the meat layer.
Step 7: Repeat the layers: add another third of the cabbage, followed by the remaining ground beef mixture, and then another third of the sauce.
Step 8: Top with the remaining chopped cabbage, and pour the rest of the tomato sauce evenly over everything. Gently stir the top layers to ensure sauce penetrates.
Step 9: Cover the slow cooker and cook on low for 6-8 hours, or on high for 4-6 hours, until the cabbage is very tender and the flavors are well blended.
Step 10: Once cooked, turn off the slow cooker and let the casserole rest for about 10-15 minutes before serving. Garnish with fresh chopped parsley, if desired.