Combine first 7 ingredients in a medium saucepan over medium-high heat. Bring to a boil. Reduce heat to low; simmer 30 minutes or until thick, stirring occasionally. Remove from heat; stir in garlic. Cool to room temperature.
Arrange bread slices in a single layer on a baking sheet; broil 1 minute or until lightly toasted. Top each slice with 1/4 cup eggplant mixture and 1 slice Brie. Broil 1 minute or until cheese melts. Sprinkle with parsley.