Put all ingredients, except the oil and vinegar, in a food processor and process until blended. Slowly mix in the oil, then mix in the vinegar. If too thick, add a little water.
Brush the leaves of romaine on both sides with the olive oil and season lightly with salt and pepper. Grill on each side for 30 seconds. Place 6 leaves on each plate, drizzle with the dressing and garnish with shaved cheese and croutons.