In a large saucepan, combine broth, potato, and onion. Bring mixture to boiling; reduce heat. Simmer, covered, for 10 minutes. Mash potato cubes against side of pan using a fork.
Stir together cornstarch and a little milk. Stir into saucepan along with remaining milk. Add broccoli and carrot. Cook and stir until thickened and bubbly. Cook 2 minutes more. Reduce heat; stir in cheese just until melted. Makes 4 servings.