Preheat the oven to 425˚. Combine the whole grape tomatoes, red onion chunks, basil and vinegar in a blender. Add 1/2 teaspoon salt and a few grinds of pepper and blend until almost smooth. Add 1/4 cup olive oil and puree until smooth. Remove 2 tablespoons of the dressing to a small bowl.
Place each steak half between 2 pieces of plastic wrap and pound on both sides with the flat side of a meat mallet until 3/4 inch thick. Season with salt and pepper and brush with the reserved 2 tablespoons dressing. Heat a large skillet over medium-high heat and add 1 tablespoon olive oil. Add the steak and sear until well browned, 3 to 4 minutes per side for medium rare. Transfer to a cutting board to rest.
Meanwhile, toss the bread chunks with the remaining 1 tablespoon olive oil on a baking sheet. Bake, tossing once, until golden, 10 to 12 minutes. Immediately toss with the grated parmesan; season with salt and pepper.
Combine the endive, radicchio, romaine, halved grape tomatoes, sliced red onion and croutons in a large bowl; drizzle with the dressing and toss. Divide among plates and top with shaved parmesan. Thinly slice the steak and add to the salads.