Slice the onions finely, then transfer them together with the oil and half of the butter to a large saucepan or pan, and let them dry gently for about 10-15 minutes, over low heat, until they become transparent.
Meanwhile, place the chicken livers in a colander and rinse them under cold running water, drain them well, and placing them on a cutting board, cut them into fairly coarse chunks. Be careful that there are no residues of blisters, in this case eliminate them and throw them away, they are very bitter! You recognize them by the dark green color.
Now combine the chicken livers with the fried onion, adding the sage, chopped rosemary and capers (along with a little of their vinegar) and sauté for about 10 minutes, then blend with the Vin Santo and let it evaporate, until when you no longer smell the wine, then add salt and black pepper.
Always keeping the heat low, start pouring the hot chicken broth a little at a time, waiting for it to dry a little before adding the other. As you combine it, mix and cook for about 40/45 minutes, with the lid off a little, until you get a thick, full-bodied but slightly creamy consistency.
Combine the remaining butter a few minutes before turning off, together with the anchovy paste, mixing carefully to mix everything.
Turn off and let them cool, then pour everything into the mixer, blending intermittently, a little at a time, in order to obtain a coarse cream. If you prefer that the pate has an even more rustic consistency, it will be sufficient to chop everything by hand with a crescent, exactly as the true Tuscan tradition would like.
Once ready, transfer the Tuscan chicken liver pate into a bowl or container, add the balsamic vinegar (my very personal touch but believe me, it really fits!) Mix and serve with toasted Tuscan bread.
Enjoy your meal!