In a 5-to-6-quart slow cooker, combine beef, garlic, oregano, rosemary, and broth. Season with salt and pepper. Cover and cook on high until beef is tender and can be pulled apart with a fork, 6 to 7 hours.
Preheat oven to 275 degrees. In a large Dutch oven, combine beef, garlic, oregano, rosemary, and broth. Season with salt and pepper. Cover and cook until beef is tender and can be pulled apart with a fork, 5 to 6 hours.
With a slotted spoon, transfer beef to a large bowl; with two forks, shred beef, discarding fat. Moisten beef with 1 cup cooking liquid; reserve remaining liquid. Refrigerate leftover beef in an airtight container, up to 5 days.
Serving Ideas: Make sandwiches: Top with red onion and mayonnaise mixed with horseradish. Use reserved cooking liquid for dipping. Mix beef with short pasta, adding more cooking liquid if needed. Serve with rice or mashed potatoes.
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