In a skillet over medium heat, add 1 tablespoon of the olive oil and toast the bread cubes, tossing frequently, until light golden brown, 3 to 4 minutes. Set aside to cool.
In a small bowl, whisk together the garlic, tamarind, Worcestershire, remaining 3 tablespoons of olive oil and salt and pepper to taste.
In a large bowl, toss the greens with the tamarind dressing.
Place 2 cups of dressed greens on each plate and top each serving with an anchovy fillet, 1 tablespoon of Parmesan, and 2 tablespoons of the croutons.