Bring a pot of water to a boil. Add the pasta and cook until very very al dente, 6 to 7 minutes. Drain and set aside.
Position an oven rack in the bottom of the oven and preheat the oven to broil.
Heat a large, heavy-bottomed ovenproof skillet over medium-high heat and add the oil. Season the chicken tenders with salt and pepper and dredge in the flour, shaking off the excess. Add the chicken to the skillet and brown on both sides until golden brown, 2 minutes per side. (Note: the chicken should only be seared, not cooked through. It will finish cooking in the oven.) Transfer the chicken to a wire-racked baking sheet.
To the same skillet, add the butter, cremini, porcini and shallots and cook, stirring minimally to aid in browning, until the mushrooms are deeply caramelized, about 15 minutes. Add the garlic and cook until fragrant, another 20 seconds. Deglaze with the marsala, scraping up any browned bits. Add the stock and bring to a simmer. Simmer until slightly thickened, about 5 minutes. Season with salt and pepper.
Off the heat, add the pasta and stir well to coat with the sauce. Top with the browned chicken, then a layer of freshly grated Parmigiano-Reggiano. Broil the pasta in the skillet until the cheese is browned and the pasta and chicken are cooked through, about 5 minutes. Sprinkle with parsley and serve immediately.