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 the fondue 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.Stirring the cheese in zigzag motions rather than in circles helps prevent the cheese from becoming stringy. A pinch of cayenne is really good in this fondue, but the cayenne specks will show on the melted cheese. Only you can decide if it's worth it or not (I think it is!) Nutrition info excludes dippers.