Cut the garlic clove in half and rub the cut sides all over the inside of a 2-quart microwave-safe casserole dish.
In the prepared dish, add the grated Swiss cheese.
Sprinkle the cornstarch and nutmeg over the cheese and toss to coat everything evenly.
Pour in the apple juice and stir until everything is thoroughly combined.
Microwave on high for 3 minutes. Carefully remove the dish (it will be hot!) and stir well.
Return the dish to the microwave and continue to cook on high in 30-second intervals, stirring well after each interval, until the cheese is completely melted and smooth. This should take about 3 more minutes.
Serve immediately in a warmed fondue pot or directly from the casserole dish with breadsticks and other dippers.