For the bread: Heat a charcoal or gas grill to medium. Brush the bread with oil and season with salt and pepper. Grill on both sides until lightly golden brown. Remove, and cut into large dice. Set aside.
For the vinaigrette: Combine the basil, vinegar, garlic, sugar and 1/4 cup water in a blender and blend until smooth. With the motor running, slowly add the oil and blend until emulsified. Season with salt and pepper.
For the salad: Put the arugula, cucumbers, olives, capers, parsley and basil in a large bowl. Add three-quarters of the vinaigrette and toss to coat the vegetables. Add the bread and toss to coat. Transfer to a large platter and drizzle with the remaining vinaigrette and EVOO. Serve at room temperature.