In a bowl, combine the tomatoes, greens, cucumber, onion and basil. In a separate bowl, combine the 1/2 cup olive oil, the 2 Tbs. vinegar, and the lemon juice. Drizzle over the tomato mixture. Season with salt and pepper and toss well.
Place half of the bread in a wide, shallow bowl. Spoon half of the tomato mixture over the bread. Layer the remaining bread on top and then the remaining tomato mixture. Cover and let sit for 1 hour.
Just before serving, toss the salad and adjust the seasonings with salt and pepper. If the bread seems dry, whisk together a little more oil, vinegar and lemon juice. Garnish with shaved cheese and serve immediately. Serves 4 to 6.