Prepare grill for direct grilling and target 400 degrees F over the direct heat.
Using a sharp boning or filet knife, carefully remove the top of the rind on one side of the brie wheel. If you only have a wedge, no need to remove.
In a 6" cast iron pan, place the brie and top with wine. Over the top of the brie sprinkle the thyme and place the pan over direct heat. Close the lid and grill for six to eight minutes or until the cheese is slightly bubbly and melting.
Remove the pan with high heat gloves and let cool. While cooling slightly add your baguette slices to the grill over direct heat and crisp up both sides. Likely no more than 2 minutes per side or until you like the crust.
Serve warm right from the cast iron pan using a small spoon. Simply spoon the cheese right onto the crostini.
See blog summary for how to make grilled crostini.