In a large salad bowl, combine the romaine, tomatoes and cucumber. Slice eggs in half; remove yolks. (Refrigerate whites for another use.)
In a blender, combine the anchovies, vinegar, lemon juice, mustard, Worcestershire sauce, garlic, sugar, pepper and egg yolks; cover and process until smooth. While processing, gradually add oil in a steady stream.
Drizzle desired amount of dressing over salad and toss to coat. Sprinkle with croutons and cheese. Refrigerate any leftover dressing for up to 3 days.