In a large nonstick saucepan, combine champagne, sugar, lemon juice and peel. Simmer, sirring occasionally, 3 minutes. Discard lemon peel.
In a medium bowl, use a heat proof stirring tool to blend cornstarch into cheese. Add to saucepan one third at a time, stirring constantly until melted, before adding next third.
Cook over medum to low heat, stirring constantly, until smooth and thickened – about 7 minutes. Stir in brandy, then pour into serving vessels. Makes about 1 ¾ cups.