In a large, heavy-bottomed saucepan, combine chicken broth and garlic over medium-high heat. Bring mixture to a simmer.

Meanwhile, in a large bowl, combine fontina, mozzarella, and cornstarch. Add cheese mixture, about 1 cup at a time, to broth mixture, stirring until cheese mixture melts before adding the next cup of cheese mixture. Reduce heat to medium, and stir constantly until cheese is completely melted. Add black pepper, white pepper, and nutmeg, stirring to combine. Remove from heat, and pour into fondue pot. Serve warm with French bread or with other desired accompaniments.