In a medium saucepan stir together milk, cornstarch, mustard, salt, and pepper.
Cook and stir over medium heat till thickened and bubbly.
Cook and stir 2 minutes more.
Add cheese; stir till melted.
Stir in ham, broccoli or cauliflower, and mushrooms.
Cook and stir till heated through.
Pour over hot pasta.
If desired, garnish with sliced green onions.