How to Make It
Preheat the oven to 350°. In a large enameled cast-iron casserole, heat the oil. Season the chicken thighs with salt and pepper and cook over moderately high heat, turning, until browned, about 5 minutes. Transfer the chicken to a plate.
Add the carrot, onion and celery to the casserole and cook over moderate heat, stirring occasionally, until golden, about 5 minutes. Stir in the tomato and cook until it breaks down and is lightly caramelized, about 5 minutes. Add the Madeira and cook until evaporated, then add the chicken stock, garlic and peppercorns. Return the chicken to the pot and bring to a simmer. Cover and braise in the oven for 1 hour, until the chicken is tender.
Using tongs, transfer the chicken to a plate to cool. Shred the meat; discard the bones. Strain the cooking liquid into
a bowl, pressing on the solids. Return the liquid to the casserole and bring to a boil. Simmer briskly until thickened to a saucy consistency, 5 to 7 minutes. Add the butter, shredded chicken and figs and cook just to warm through.
Meanwhile, in a pot of salted boiling water, cook the pasta until al dente. Drain, reserving 1/2 cup of the pasta water. Add the pasta and reserved pasta water to the casserole and toss. Remove from the heat and stir in the Parmigiano and tarragon. Serve in bowls topped with the almonds and Manchego shavings.