To prepare dressing, combine shallots, lemon juice, mustard, salt, and black pepper. Gradually add oil, stirring with a whisk.
To prepare salad, combine arugula and 1 tablespoon dressing; toss to coat. Arrange 1/2 cup arugula mixture onto each of 4 salad plates. Combine Belgian endive, radicchio, and remaining dressing; toss to coat. Arrange about 1 cup endive mixture evenly over each serving. Top each serving with 1 1/2 teaspoons cheese. Serve salad immediately.