In a medium bowl, combine the balsamic vinegar, extra virgin olive oil, Dijon mustard, Worcestershire sauce, finely chopped basil, and minced garlic. Whisk together until well combined and emulsified. Set aside.
Preheat your oven to 375°F (190°C). Spread the seasoned Italian bread cubes on a baking sheet. Drizzle with a tablespoon of olive oil and toss to coat. Bake for about 10-15 minutes, or until golden and crispy. Remove from the oven and sprinkle with grated Parmesan cheese while warm.
In a large salad bowl, combine the torn romaine lettuce, iceberg lettuce chunks, sliced red onion, and pitted black olives. Toss gently to mix.
Add the finely chopped hard-boiled eggs to the salad. Drizzle the prepared balsamic dressing over the salad and toss gently to coat.
Top the salad with homemade Parmesan croutons and the remaining grated Parmesan cheese. Give it one last gentle toss and serve immediately.