Place the grated cheeses in a large bowl. Toss them with the cornstarch, dry mustard, garlic powder, and white pepper.
Pour the wine into the fondue pot. Turn the temperature to setting 5 (medium-high) and bring the wine to a strong simmer (bubbling, but not boiling strongly). This should take 1-2 minutes.
Stirring constantly with a wooden skewer in zigzag (not circular) motions, add the cheeses, a handful at a time, waiting for each handful to melt completely before adding another.
Reduce the temperature to 3 (medium-low) and serve with your choice of dippers.
It's best to shred the cheeses 30 minutes ahead of time and let them slightly dry up, making it easier to evenly coat them with the cornstarch and spices.If the fondue seems stringy, stir in a teaspoon of fresh lemon juice. You can also add it as a preventative when you add the wine to the pot.Nutrition info excludes dippers.