In a medium-sized stainless steel or glass bowl, combine the egg yolks, minced garlic, anchovy paste, Dijon mustard, lemon juice, and Worcestershire sauce.
Whisk the ingredients vigorously until the mixture is well-combined and begins to look slightly frothy.
Place the bowl on a damp kitchen towel to stabilize it. While whisking constantly, begin adding the oils drop by drop.
Once the emulsion begins to thicken, continue adding the oil in a very slow, steady, thin stream until all the oil is incorporated and the dressing is thick and creamy.
Fold in the finely grated Parmigiano-Reggiano cheese using a whisk or spatula.
Taste and season with kosher salt and black pepper as needed.
If the dressing is too thick, whisk in a teaspoon of warm water to reach the desired consistency.
Serve immediately or refrigerate in an airtight container for up to 2 days.