Prepare a large bowl with ice and cold water, set aside to blanch the asparagus.
Bring a saucepan big enough to hold the asparagus to a boil, add a heaping tablespoon of salt and plunge the asparagus into the water, boil for 2 minutes. Drain the asparagus and put into the water bath until cooled, drain and set aside on a baking sheet covered with paper towels.
Combine mayonnaise, vinegar, lemon juice, garlic, Dijon mustard, Worcestershire sauce, and anchovy paste in a medium bowl and whisk until combined. While whisking constantly, add the olive oil in a thin, steady stream until incorporated. Season to taste with salt and pepper.
Toss the romaine with a little of the dressing. Transfer to a serving platter and top with asparagus and the grated Parmigiano-Reggiano. Serve extra dressing on the side.