Combine first 5 ingredients in a small bowl; rub oregano mixture evenly over beef. Heat a large Dutch oven over high heat. Coat pan with cooking spray. Add beef to pan; cook 3 minutes on each side or until browned. Add 1 cup water and garlic to pan, scraping pan to loosen browned bits. Cover and bake at 300° for 3 hours or until beef is very tender. Cool to room temperature. Cover and chill 8 hours or overnight.
Skim fat from surface of broth. Remove beef; shred with 2 forks. Return beef to pan; bring to a simmer over medium-high heat. Simmer mixture 3 minutes or until liquid evaporates; stir in lime juice. Reduce heat to medium, and cook beef 3 minutes or until crisp in spots.