How to Make It
Bring a small saucepan of water to a boil. Plunge the tarragon into the water and cook just until wilted but still bright green. Drain the tarragon and refresh under cold water. Pat the tarragon dry with paper towels and transfer to a blender or food processor. Add 3/4 cup of the olive oil and a pinch of salt and blend until smooth.
Meanwhile, light a grill or heat a grill pan. Combine the remaining 3 tablespoons of olive oil with the vinegar and add a generous pinch each of salt and pepper. Brush the endives with the oil and vinegar mixture and grill over a medium-low fire for about 12 minutes, turning, until softened and slightly charred. Arrange the endives on a serving platter.
Pour the tarragon oil over the endives. Using a vegetable peeler, shave the Pepato over the endives. Serve warm or at room temperature.