Fill a large pot with lightly salted water and bring to a rapid boil. Add egg noodles and cook at a boil until tender yet firm to the bite, 7 to 9 minutes. Drain.

Combine drained noodles, chicken, ham, and Swiss cheese in a large mixing bowl; mix until well combined.

Stir together cream of chicken soup, milk, and sour cream in a separate bowl until smooth. Pour sauce over noodles and mix until sauce is well distributed. Transfer mixture to a large microwave-safe casserole dish.

Place butter in a microwave-safe bowl. Cook on high until melted, about 30 to 45 seconds. Add bread crumbs and Parmesan cheese. Mix until well blended and crumbly and sprinkle on top of casserole.

Microwave casserole uncovered for 10 minutes. Allow to cool for 5 minutes before serving.