Create a slurry with the cornstarch and Kirsch and set aside briefly. Cut the chilled brie into small pieces.
Rub inside of a saucepan with the garlic clove. Over medium heat bring Champagne and lemon juice to a gentle boil. Reduce heat to low and stir in the brie. Blend the cornstarch/Kirsch slurry into the cheese pot and stir for a couple of minutes until the mixture is smooth and thick. Transfer to a fondue pot over a flame and season with white pepper. Serve with bread cubes on fondue forks.