Melt butter in a heavy saucepan over low heat.
Add shallots and cook until soft.
Add wine and bring to boiling to reduce by half.
Add whipping cream; simmer 5 minutes.
Combine cornstarch with cheese and add to saucepan, stirring constantly until melted. Do not boil. Season with salt to taste.
Pour mixture into fondue pot. If necessary, thin fondue with additional white wine until desired consistency is reached.
Serve with bread cubes or raw vegetables.