Prepare the tapenade by combining all the ingredients for it in a food processor with a little of the olive oil. Pulse until you have a smooth paste. Add the remaining olive oil to adjust the consistency if desired and season to taste. Transfer to a bowl, cover and set to one side.
Slice the polenta into triangles and arrange on a lined baking sheet. Brush very lightly with the olive oil, then season. Pre-heat the grill to hot.
Grill the polenta in batches, turning occasionally, until lightly coloured on both sides. Remove and spread each slice with a little of the tapenade. Arrange on a serving platter and garnish with a sprig of parsley before serving.