1. Heat the oven to 350°. Toast the pine nuts in the oven until they are golden brown, about 8 minutes.
2. In a small stainless-steel saucepan, combine the raisins, broth, and vermouth. Bring to a boil and simmer until reduced to about 3/4 cup, about 8 minutes. Set aside.
3. In a large frying pan, melt 1 tablespoon of the butter with 1 tablespoon of the oil over moderately high heat. Season the livers with 1/4 teaspoon of the salt and 1/8 teaspoon of the pepper and cook, in two batches if necessary, until almost done, about 3 minutes. The livers should still be quite pink inside. Remove them from the pan.
4. Add the remaining 1 tablespoon oil and 1 tablespoon butter to the pan and reduce the heat to moderately low. Add the garlic and cook, stirring, for 30 seconds. Add the flour and cook, stirring, for 15 seconds longer. Stir in the raisin-and-vermouth mixture and the remaining 1/4 teaspoon salt and 1/8 teaspoon pepper. Bring to a simmer, scraping the bottom of the pan to dislodge any brown bits. Add the livers and any accumulated juices, the pine nuts, and the parsley and simmer until the livers are just done, about 1 minute longer.
Wine Recommendation: Try matching the savory tastes of this Sicilian-flavored dish with a rustic red wine that hails from the same region. Or serve the easy-to-find Salice Salentino from Apulia, also in Southern Italy.