In a medium bowl, combine the shallots, balsamic vinegar, and red wine vinegar. While stirring with a spoon, drizzle in the extra-virgin olive oil. Add the tomatoes, basil, parsley, 1 teaspoon salt, and 1 teaspoon pepper. Mix well to combine, and set aside.
Arrange 2 wedges of iceberg lettuce against each other on each of 4 serving plates. Season the iceberg lettuce with the remaining 1/4 teaspoon salt and 1/4 teaspoon black pepper. Sprinkle 1/4 cup grated mozzarella and 1/4 cup blue cheese over each plate. Then generously spoon the tomato vinaigrette over all, dividing it evenly among the salads.