In a blender or food processor, combine anchovy fillets, Worcestershire, vinegar, garlic, paprika, dried oregano, and pepper. Whirl until smoothly puréed, scraping container sides as needed. With motor running at high speed, pour in the oil.
Break romaine leaves into bite-size pieces and put in a wide bowl. Shell eggs, and shred or finely chop and add to lettuce along with croutons and parmesan cheese. Add anchovy dressing (about 6 tablespoons) and lemon juice to taste, and mix well.