Chill brie round for one hour to help make it easier to remove the rind. 

Slice away the rind and cut the remaining cheese into rough chunks.

Add the cornstarch or arrowroot flour to a bowl and toss in the brie chunks. Turn to coat evenly. Set aside.

Melt butter in a medium saucepan over medium-low heat. 

Add shallot and garlic; saute for 2 minutes. Add wine and heat through, stirring, until gently simmering.

Gently add the coated chunks of brie. Mix with a wooden spoon as it melts, which can take up to 15 minutes on medium low. 

Add thyme. Season to taste with pepper. Stir.

Pour melted brie mixture into a fondue pot. Stir occasionally.

Serve with hearty cubes of artisan bread or baguettes, apple and pear slices or thick slices of cooked sausage or bratwurst.