In a food processor, blend the anchovies, egg, garlic, lemon juice, Worcestershire sauce,, Dijon mustard, cayenne pepper, salt, and pepper. Blend on high for 10 seconds.
Slowly pour in the olive oil while continuing to blend. Slowly is important here. The oil should meld with the dressing (but it's ok is some does not). Blend until smooth.
Add in the Parmesan cheese and pulse blend for 3 to 5 seconds to combine.
In a bowl add the romaine lettuce, then pour 80% of the dressing over top. Toss to coat.
Plate the salad, then top with the grilled chicken strips, extra grated Parmesan cheese and croutons. Drizzle with the remaining salad dressing.
Serve.
Notes
For less heat, decrease the amount of cayenne pepper powder used or substitute in crushed red pepper.