Preheat oven to 325 degrees Fahrenheit.
Heat olive oil in large dutch oven.
While oil is heating, coat lamb with salt, pepper and rosemary.
Add chopped onions to heated oil and saute 2-3 minutes. Add garlic and cook one additional minute until fragrant.
Add lamb and cook until browned on one side (about 3 minutes). Flip and brown other side. Remove meat and vegetables from pan onto a plate temporarily.
Slowly pour wine to dutch oven and reduce heat to low. Scrape brown bits from bottom of pot.
Add meat and vegetables back to pan. Add broth, carrots, and thyme. Turn off heat.
Cover dutch oven with lid. Cook in oven for 2 hours and flip meat. Increase heat to 400 degrees and cook for an additional 1 hour.
When meat reaches desired doneness, remove from oven and shred lightly with fork. If desired, serve with the cooked carrots and/or over potatoes.