In a large pan, heat olive oil over medium heat. Add onions and garlic, and cook, stirring, until onions begin to soften, about 3 minutes. Stir in tomatoes and vinegar. Dissolve tomato paste in the broth and add to onions and tomatoes. Add basil and sage. Season with salt and pepper, and simmer until the sauce has thickened, 15 to 20 minutes.

Add beans to the tomato sauce. Cook, stirring, to combine and heat through, about 15 minutes.

To prepare polenta: In a heavy pot, combine polenta with 1 tablespoon salt. Turn heat to medium and gradually whisk in 9 cups cold water, stirring constantly, until polenta begins to boil. Lower heat and simmer, stirring frequently with a wooden spoon, until thick, about 45 minutes.

If using pancetta: Place pancetta in a small saucepan over low heat. Cook, stirring frequently, until the pancetta is brown and crisp, about 15 minutes. Use a slotted spoon to transfer pancetta to a paper towel to drain.

To serve, spoon polenta into serving dishes. Ladle the beans over the polenta and top with pancetta, if using. Garnish with fresh herbs.