Preheat oven to 350F. Cook vegetables separately in boiling salted water 5 minutes. Drain thoroughly. Distribute evenly in a lightly buttered casserole. Beat eggs. Combine with mayonnaise, onion, mushroom soup, and 1/2 cup grated cheese. Pour evenly over vegetables. Sprinkle remaining cheese over top and level evenly. Pour melted butter over top of casserole. Distribute crushed croutons over melted butter.
Bake 40 minutes.
Should be prepared early in the day (or even the day ahead) so the flavours blend and the topping mellows. Bake again just before serving to heat through.