This salad holds up well when dressed, making it ideal for a party.
Preheat oven to 400 degrees. Tear bread into bite-size pieces, and toss with 3 tablespoons oil. Season with salt and pepper. Bake on a rimmed baking sheet until golden brown, about 9 minutes.
Whisk together mustard, shallot, lemon juice, basil, and remaining 1/2 cup oil. Season with salt and pepper.
Trim core ends of salad greens. Cut romaine heads in half lengthwise, and radicchios and endives into quarters lengthwise. Place half the wedges on a platter, and drizzle with 1/4 cup dressing. Top with remaining wedges, and drizzle with another 1/4 cup dressing. Scatter with cheese and croutons, and serve remaining dressing on the side.