1. Combine first 6 ingredients in a food processor; pulse until finely chopped. Peel and section lime over a bowl, catching juices; discard peel. Add lime juice, lime sections, and 1 tablespoon olive oil to food processor; process until smooth. Scrape the chipotle mixture into a zip-top plastic bag. Add pork; seal. Marinate in refrigerator 1 hour.
2. Preheat oven to 325°.
3. Heat a small Dutch oven over medium-high heat. Add 1 tablespoon oil to pan; swirl. Remove pork from bag; reserve marinade. Sprinkle pork with salt. Add pork to pan; sauté 8 minutes, browning on all sides. Remove pork from pan. Add broth and reserved marinade to pan; bring to a boil, scraping pan to loosen browned bits. Return pork to pan; cover and bake at 325° for 2 1/2 hours or until pork is fork-tender. Shred pork; toss with sauce.