Rub the inside of the fondue pot with the garlic halves. Finely chop the garlic and sprinkle into the pot. Add wine; heat until wine is slightly warm. Add cheeses; melt over medium heat, stirring constantly. Do not let the cheese mixture boil.
In a small bowl, combine cornstarch and liqueur; stir into cheese mixture. Season with nutmeg and white pepper. Place pot over an alcohol burner or small candle. Stir occasionally; do not let mixture boil.
Cut bread into 1-1/2" cubes. Dip cubes of bread into cheese, using a fondue fork, letting bread soak up as much cheese as possible.