Preheat the oven to 400 degrees F.
Bring 1 1/2 cups water to a boil in a pot and season with salt. Add the cauliflower, cover and steam until just tender, 7 to 8 minutes. Drain and cut into florets.
Meanwhile, bring another pot of salted water to a boil and cook the noodles to just shy of al dente, about 5 minutes. Drain.
Heat 4 tablespoons butter in a large skillet over medium heat. Add the mushrooms and cook until tender and browned. Add the garlic and shallots and cook, stirring, for 2 to 3 minutes. Add the flour and cook, whisking, for 1 minute. Deglaze with the sherry, stirring and scraping up any browned bits with a wooden spoon. Whisk in the chicken stock and bring to a boil. Reduce the heat to a simmer and cook for a few minutes, then stir in the heavy cream. Season with salt, pepper and a few grates of nutmeg.
Combine the cauliflower, noodles, chicken and sauce. Transfer to a casserole dish.
Melt the remaining 4 tablespoons butter in small pan, then drizzle over the panko in a bowl and toss to combine. Add the Parmigiano-Reggiano and toss. Sprinkle the breadcrumbs over the casserole. Bake until hot, bubbling and golden, 40 to 45 minutes. Sprinkle with the parsley. Divide among plates.
Cook's Note: The unbaked casserole (without the breadcrumbs) can be covered and refrigerated for a make-ahead meal.
Put the chicken in a very large stockpot or divide between 2 pots if necessary. Add the peppercorns, garlic, bay leaves, carrots, celery, lemons, onions and herb bundle and sprinkle with salt. Add enough water to cover the chicken. Bring to a boil, then reduce the heat to low and cook at a rolling simmer for 1 1/2 hours. Remove the chicken from the liquid and let cool. Strain the stock. (You should have 5 to 6 quarts stock.) Remove the skin and bones from the chicken, and shred the meat using your hands or 2 forks.