Heat the oven to 375°F. Place chicken in a saucepan with poaching water and chicken salt, bring to a gentle simmer, cover and cook for 20 to 25 minutes until at least 165°F. Drain and shred into short pieces.
Meanwhile, cook mushrooms in oil in a large skillet for 9 to 11 minutes until browned and dry. Boil fusilli in water with the tablespoon salt until 3 minutes short of the package time; reserve 3/4 cup pasta water and drain.
Add 2 tablespoons butter and garlic to the mushrooms and stir for 30 seconds. Add cream, milk, sauce salt and pepper and simmer gently for 2 minutes.
Remove from heat and stir in Parmesan, then fold in pasta and chicken with 1/2 cup reserved pasta water. Transfer to a deep 9-by-13-inch baking dish and cover with foil.
Bake for 20 minutes. Melt the remaining tablespoon butter and mix with panko, then uncover the dish and scatter crumbs over it.
Bake uncovered for 8 to 10 minutes until crumbs are golden and the center reaches 165°F. Rest for 5 minutes; add a little remaining warm pasta water around the edges only if the sauce looks dry.