Heat a large skillet over medium-high heat. Add the beef cubes in a single layer and brown on all sides, about 5 minutes total. Transfer the beef to the slow cooker.
Add the sliced mushrooms, diced onion, and minced garlic to the same skillet. Cook for 3 minutes, stirring often, then scrape everything into the slow cooker.
Pour in the crushed tomatoes, tomato paste, and beef broth. Stir in the oregano, basil, rosemary, bay leaves, salt, and pepper until the tomato paste is fully mixed.
Cover and cook on low for 8 hours or on high for 4 to 5 hours, until the beef is fork-tender.
Remove the bay leaves before serving. Ladle the stew into bowls and top with grated Parmesan and fresh parsley.