In a saucepan, heat 1 tablespoon olive oil over medium heat. Add onion and rosemary, cover, and cook until onion is tender, about 6 minutes. Add garlic, cook 1 minute more.
Place carrots in bowl, cover, and microwave 4 minutes. Stir broth, beans, tomatoes, and cooked carrots into saucepan with onions; bring to a boil, reduce heat, and simmer 10 minutes. Remove 1 cup of bean mixture, cool, and puree in blender or food processor; add back to saucepan.
Meanwhile, heat remaining 1 tablespoon olive oil in a large skillet over high heat. Add pork in small batches and cook, turning once, until browned and cooked through (6 minutes). Serve bean mixture over sliced pork.
