Step 1

Soak beans in water overnight. Drain, and transfer to a large pot. Cover beans with 4 inches water. Add the intact half of the onion, the carrot, celery, and bay leaf. Bring to a boil. Reduce heat, and simmer until beans are tender but not bursting, about 1 hour. Drain, and remove onion, carrot, celery, and bay leaf; discard.

Step 2

Pulse tomatoes, with juice, in a food processor until coarsely chopped. Heat oil in a medium heavy-bottomed pot over medium heat. Add chopped onion, the garlic, and red-pepper flakes. Cook, stirring occasionally, until onion and garlic are tender but not browned, about 3 minutes. Add tomatoes and rosemary. Bring to a boil.

Step 3

Add beans, and simmer, stirring occasionally, until tomato sauce thickens, about 20 minutes. Season with salt and pepper. Serve warm, and drizzle with oil just before serving.