Place barley into a bowl and cover with several inches of cool water; let stand for 1 hour. Drain.
Heat the oil in a heavy-bottomed saucepan over medium-high heat. Add pancetta and cook until slightly crisp, about 3 or 4 minutes. Stir onion, carrot, and celery into pancetta and cook until vegetables are slightly softened, 2 to 3 minutes.
Mix half of the beans into vegetable-pancetta mixture and pour in enough water to cover; stir in barley and remaining beans. Season mixture with salt and pepper. Bring liquid to a boil, reduce heat to medium-low, and simmer for 40 minutes, stirring regularly and adding more water if soup gets too thick.
Remove saucepan from heat and allow to sit for 5 minutes. Serve soup with rosemary leaves and a drizzle of olive oil.