Add all ingredients (except potatoes) to a blender with a splash or two of water. blend until smooth, then transfer to a small ziplock plastic bag.
Preheat the oven to 400F.
Line a baking sheet with parchment paper. Add potato halves and toss with olive oil.
Sprinkle with sea salt and pepper.
Bake for 30-35 minutes until brown, flipping halfway in-between. Remove from heat and squeeze tapenade on top of each potato to serve.