In a medium saucepan, heat the pure olive oil until shimmering. Add the onion and rosemary and cook over moderate heat, stirring occasionally, until the onion softens, about 5 minutes. Add the beans, stock, water, carrot and bay leaf and bring to a boil. Cover partially and simmer over moderately low heat until the beans are tender, about 45 minutes. Season the beans with salt and pepper and simmer for 10 minutes longer.