Regionally, this braised dish can be prepared with or without chili pepper, with rabbit or dark chicken and with various add-in vegetables. My favorite basic recipe is the classic by Marcella Hazan from her Essentials cookbook: chicken, onion, garlic, wine, tomatoes, salt and pepper--basic and delicious. In my recipe, I love to use earthy mushrooms like lots of sautéed meaty cremini or portobellos or--even better and bigger in flavor--reconstituted porcini and their rich broth. Many Italian-American versions of the classic also include sweet or frying peppers. If I use red frying or stuffing peppers, I like to roast and peel them for a smoky addition.
Place mushrooms in a small pot and cover with stock. Bring stock to a boil and reduce heat to low simmer to reconstitute mushrooms.
Season the chicken with salt and pepper on both sides and dredge lightly in flour.
Heat olive oil in a large Dutch oven over medium-high heat and brown the chicken in 2 batches until crispy on both sides. To the pan drippings, add onions, garlic and red pepper, and stir to soften 5-6 minutes. Add wine to deglaze the pan and let reduce by half. Add tomatoes and break them up; stir in a few leaves of basil.
Remove the mushrooms from the stock with a slotted spoon; chop them and add them to the sauce. Add all of the mushroom stock except for the last 2 tablespoons or so to prevent any sediment from the mushrooms from getting into the pan. Simmer sauce 20-30 minutes at a gentle bubble to thicken a bit.
Add chicken back to the sauce and simmer 20-30 minutes more to cook chicken through. If serving as a main dish and the pasta as a first course, remove chicken to a warm serving platter and cover to keep warm. If you are serving the pasta as a side dish, this is not necessary.
While the chicken cooks, bring a large pot of water to a boil. Salt water and cook pasta to al dente
. Reserve about 1/2 cup starchy cooking liquid and drain pasta. Return it to the pot and toss with starchy water, butter, about 1/3 of chicken and mushroom sauce, and the parsley. Toss to combine and emulsify. Adjust salt and pepper to taste; transfer to warm serving bowl and top with a little more sauce and Pecorino cheese.
Top the chicken with a little extra sauce and pass any remainder at table in gravy boat. If you are serving the chicken as a main course separate from the pasta, round out the meal with green beans and or a salad of arugula and red onion.