Preheat oven to 350 degrees F (175 degrees C). Butter a casserole dish.
Melt butter in a saucepan over medium heat; whisk in flour until smooth. Stir mushroom soup, water chestnuts, and dry mustard into butter mixture; cook, stirring often, until mixture is hot, about 3 minutes.
Layer half the egg slices, half the asparagus, and half the soup mixture in the prepared dish; repeat layers. Sprinkle top of casserole evenly with onion rings; sprinkle cheese over onion rings.
Bake in the preheated oven until bubbly, about 30 minutes.