Combine vegetables, chicken broth, salt, and pepper in a saucepan.
Cook until vegetables are barely tender.
Melt butter in a separate, larger saucepan.
Add flour a little at a time mixing until well blended.
Gradually add milk.
Stir until thickened over medium heat.
Add cheese and stir until melted.
Add vegetables and desired amount of chicken broth from vegetables.
Season to taste.