If you’d like to make this comforting dish ahead of time, you can freeze the unbaked casserole up to three months. Let it thaw completely; top with Parmesan and panko, then bake at 350°F until browned and bubbly, about 45 minutes.
Bring a large pot of water to boil over high. Add pasta; reduce heat to medium-low, and cook until noodles are al dente, 8 to 9 minutes.
Meanwhile, heat oil in a 5- to 6-quart Dutch oven over medium-high. Add onion and celery; cook, stirring occasionally, until softened, about 5 minutes. Add mushrooms; cook, stirring occasionally, until liquid has evaporated, 7 to 8 minutes. Reduce heat to medium.
Drain pasta, reserving 1/4 cup cooking liquid; set aside. Stir sherry into mushroom mixture, gently scraping to loosen browned bits; stir in butter until melted. Add flour; cook, stirring constantly, until smooth, 1 to 2 minutes. Add broth and reserved cooking liquid; cook, stirring, until liquid begins to thicken, about 3 minutes. Stir in 1/2 cup Parmesan, cream cheese, and salt; cook, stirring constantly, until smooth, about 2 minutes. Remove from heat. Add chicken and cooked pasta; stir to coat.
Preheat broiler to high. Transfer pasta mixture to a deep 3-quart baking dish. Top with panko and remaining 1/4 cup Parmesan. Broil until top is golden, 2 to 3 minutes. Remove from oven; garnish with parsley.