Heat oven to 375°F. Cook spaghetti with tablespoon salt to 2 minutes short of package time; drain.
Meanwhile, season chicken with its salt and pepper. Heat oil in large skillet; cook chicken 7 to 8 minutes to at least 165°F. Plate; cook mushrooms and onion 7 to 8 minutes until water evaporates.
Add 2 tablespoons butter and flour; stir 1 minute. Gradually add sherry, broth, and milk; simmer 4 minutes until lightly thickened. Fold in chicken, peas, Parmesan, and pasta.
Transfer to deep 9-by-13-inch, 4-quart dish. Melt remaining butter; toss with panko and scatter over. Loosely foil-cover.
Bake 20 minutes, then uncovered 10 to 12 minutes until crumbs golden and center 165°F. Rest 5 minutes.