Rub the inside of a heavy pot or dutch oven with the cut side of the garlic. Add beer and mustard and bring to a simmer over medium heat.
In a bowl, toss the cheese with the cornstarch. Working in 3 batches, gradually stir the cheese mixture into the beer until melted. Pour in the kirsch and cook, stirring occasionally, until the mixture is gently bubbling, about 2 minutes; season.
Serve immediately from the dutch oven or transfer to a fondue pot. Top with grated nutmeg to taste. Serve with hard or soft pretzels broken into pieces.