Bring a small pot of water to a gentle simmer. Lower the whole egg in for 60 seconds, then transfer to an ice bath. Separate the coddled yolk into a small bowl.

In a food processor, combine the coddled egg yolk, garlic, anchovy paste, lemon juice, Dijon mustard, and Worcestershire sauce. Pulse until smooth, about 15 seconds.

Add the mayonnaise and grated parmesan; pulse to combine. With the processor running, slowly drizzle in the olive oil until the dressing is thick and glossy. Refrigerate while you make the croutons.

Toss the cubed bread with 2 tablespoons olive oil, 1 minced garlic clove, and ¼ teaspoon salt. Spread on a sheet pan and bake at 375°F for 10–12 minutes, tossing halfway, until golden and firm.

Add the chilled, chopped romaine to a large bowl. Pour ¾ of the dressing over and toss thoroughly with tongs until every leaf is coated, adding more dressing as needed.

Top with croutons, shaved parmesan, and a generous crack of black pepper. Serve immediately.