Heat olive oil in a large pot or deep casserole and add the onion. Cook on low heat until soft, about 5 minutes.
Stir in carrot and celery and cook another 5 minutes.
Add the garlic and stir briefly until fragrant, about 30 seconds.
Pour in the wine and cook until it has almost evaporated. (Turn the heat up if you want to speed the process.)
Mix in the tomatoes, sage, beans, broth, farro, and salt and pepper. Bring to a boil and then lower the heat and simmer for an hour.
Puree coarsely using an immersion blender, a regular blender, or food processor.
Ladle into bowls and top with shaved or grated Parmesan, if desired.
Notes
If you prefer not to use the wine in step 4, juice half a lemon and then, add enough water to make half a cup. Taste after pureeing; add ½ teaspoon or more sugar if it is too tart.This recipe is adapted from Farro and Bean Minestrone in The Silver Spoon, a compendium of Italian cooking from Phaidon Press (2015).