Grate all of the cheeses. In a medium bowl, combine the cheeses with the cornstarch, tossing thoroughly to coat all pieces.
In a stove-safe fondue pot or large heavy saucepan, bring the wine, garlic, and lemon juice to a simmer over medium-low heat. Add the cheeses to the simmering liquid a little at a time, stirring well between each addition to ensure a smooth fondue. Once smooth, stir in the brandy, mustard, and nutmeg.
Serve with cooked meat, bread, broccoli, potatoes etc