In a large nonstick saucepan, melt butter. Add shallots and cook, stirring occasionally, until tender but not browned – about 5 minutes.
Add wine, tarragon and vinegar, reduce heat to low and simmer 3 minutes.
In a large bowl, combine cheeses and cornstarch, toss until well coated.
Add cheese to the saucepan a handful at a time, stirring after each addition until melted.
Cook over medium-low heat, constantly, until smooth and thickened – about 10 minutes.