Whisk the mustard and the vinegar together in a mixing bowl. Whisking constantly, add 2-3 tablespoons of the oil in a thin stream until the mixture thickens. Then in a steady stream, whisk in the remaining oil. Season with salt and pepper to taste. If desired, you can thin the vinaigrette by whisking in a few drops of water.

Preheat a gas grill to medium high, or preheat a grill pan on top of the stove to medium. Grill the radicchio and endive, uncovered, until they begin to wilt and char but are still holding their shape, 5 to 7 minutes, turning occasionally and brushing with the dressing leftover in the bottom of the mixing bowl. Place the radicchio and endive in a large bowl and add the vinaigrette and oregano. Toss to coat.