Grate all of the cheeses.
In a medium bowl, combine the cheeses with the cornstarch, tossing thoroughly to coat all pieces.
In a large heavy saucepan, bring the wine, garlic, and lemon juice to a simmer over medium-low heat.
Add the cheeses to the liquid mixture a little at a time, stirring between each addition to ensure a smooth fondue. Once smooth, stir in the brandy, mustard, and nutmeg.
Arrange an assortment of bite-size dipping foods on a platter. If necessary, carefully pour the fondue into a fondue pot. Dip and enjoy!