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1
Heat oven to 325 F. Soak the livers in milk for one hour, then drain, pat dry, trim, roughly chop, and set aside. Rinse chicken thighs and pat dry, then lightly dredge in flour, shaking off excess. Set aside. Bring the chicken broth just to a boil, then remove from heat. Take a handful of the dried porcini (enough to yield 1 1/2-2 tsp) and grind to powder in a spice or coffee grinder and set aside. Put remaining dried porcini in a large bowl and reconstitute with the broth. (Cover and set aside to steep while you do the rest of your prep. When ready to start cooking, remove the porcini from the broth and rinse, then set on a towel to dry. Strain the mushroom-infused chicken broth through fine-mesh sieve lined with cheesecloth or paper towels to remove grit. Put the broth in a saucepan with the parmigiano heel, cover, and let slow-jam on a back burner over a very low flame until ready to use.)
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2
Film a large, oven-safe skillet or saute pan with oil. Brown thighs on both sides in oil (in batches if necessary) over medium/medium-high heat, about five minutes per side. Remove to a plate, cover, and set aside. Add butter to the pan. When foaming subsides, add livers and prosciutto and saute a couple minutes, til browned and aromatic, then add onion, carrot, fennel, and parsley, and cook until they start to soften and the onion turns translucent. Add the rehydrated porcini and the cremini mushrooms, raise the heat, and saute until the mushrooms give up their liquid and start to brown. Lower heat slightly and add the ground fennel seed, thyme, sage, and reserved porcini powder, and saute about a minute to cook off their raw taste. Add the tomato paste and let it take on some color, stirring constantly to prevent scorching. Raise the heat to high and deglaze with the marsala or sherry, stirring to scrape up browned bits. When the marsala is about half-reduced, add the tomatoes and the mushroom-chicken broth and bring to a boil. Nestle in chicken thighs, skin-side up, cover, and transfer to the oven. Braise until chicken is falling-off-the-bone tender, about 1 1/2 hours.
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3
When the chicken is cooked to the desired tenderness, remove the pan from the oven. Fish out the thighs with tongs and set aside til cool enough to handle. Meanwhile, put the pan over medium-low heat on the stovetop, and allow the sauce to simmer down and tighten up a bit. When chicken is cool enough to handle, remove skin, bones, and gristle, and roughly shred the meat by hand. Return to the sauce, along with the heavy cream, if using, and heat through. Garnish with parsley and serve with gnocchi; with something ridged and tubular such as rigatoni; or with something ribbony like pappardelle or malfatti (which you can make by smashing up lasagna sheets into smaller, bite-size pieces).
