Heat wine, garlic, and thyme over medium-low heat in a heat-safe fondue pot. Bring to a simmer.
Toss grated cheese in cornstarch until evenly coated (to prevent clumping).
Add grated cheese into the liquid mixture one handful at a time then stir until melted. Add a handful at a time and stir in between to melt until all the cheese is melted and smooth.
Once the cheese is melted and smooth, stir in brandy, mustard powder, paprika, salt, pepper, and nutmeg until incorporated. Transfer the pot to the warmer and serve immediately with the various dippers.Using fondue forks or wooden skewers, dunk the dippers into the melted cheese and enjoy! Store leftovers in an airtight container in the refrigerator for 4-5 days.