Stir together first 5 ingredients in a small bowl until well blended. (The goat cheese mixture can be prepared up to 1 day ahead.)
Cut 2 rounds out of each bread slice using a 1 1/2-inch round cutter. Spread olive mixture evenly on 1 side of half of bread rounds, top with remaining bread rounds. Roll sides in chopped parsley. Cover and chill 2 hours before serving.
Note: For testing purposes only, we used Pepperidge Farm Very Thin White Bread Slices.