In a small sauce pan, combine all ingredients except Brie. Stir to combine. Bring to a gentle boil, then turn the heat to low. Allow to simmer 5-7 minutes, until thickened.
Remove the top rind from the Brie. (About 1/8" off the top.) Place the Brie in an oven safe baking dish, exposed cheese side up. Pour dried apricot sauce on top of the Brie, and bake for 10 minutes, until Brie is very soft and melty.