Fill a large pot three-quarters full of water and bring to a boil. Add the pasta and cook until al dente, about 10 minutes, or according to package directions.
While the pasta cooks, preheat an oven to 375°F Coat a 3-qt baking dish with nonstick cooking spray.
In a large saucepan over medium-high heat, whisk the cornstarch and evaporated milk until blended. Add the chicken broth and pepper. Bring to a boil, whisking frequently, then reduce heat to low. Simmer, whisking frequently, until the sauce has thickened slightly, about 5 minutes.
Stir in the mushrooms and carrot, partially cover the pan, and simmer until the vegetables are tender, about 5 minutes.Stir in the sherry, nutmeg, pepper sauce, and chicken.
Drain the pasta and put it in the prepared baking dish. Add the sauce and toss to combine. Sprinkle with the bread crumbs and cheese. Bake until the topping is lightly browned and the sauce is bubbling, 25-30 minutes. Cool 5 minutes before serving.