Place anchovy fillets and garlic cloves in a small food processor or blender. Pulse until they form a smooth paste, scraping down the sides as needed (about 30–45 seconds).

Emulsify base

Add the mayonnaise, Greek yogurt, Dijon mustard, Worcestershire sauce, lemon juice, and olive oil to the anchovy‑garlic paste. Pulse or whisk until well combined and smooth (about 30 seconds with a processor or 1–2 minutes by hand).

Incorporate cheese and season

Stir in the freshly grated Parmesan cheese and (if using) Pecorino Romano until evenly distributed. Taste and season with sea salt and freshly ground black pepper. If dip tastes too thick or sharp, add an additional 1 teaspoon lemon juice or 1–2 teaspoons cold water to adjust consistency and brightness.

Adjust texture and chill

If you prefer an extra-smooth texture, briefly run the mixture in the food processor one more time. Transfer the dip to a bowl, cover tightly, and refrigerate for at least 30 minutes to let flavors meld (up to 24 hours).

Finish & Serve

Garnish

Before serving, stir in chopped fresh parsley and sprinkle with a pinch of cracked red pepper flakes if you want a little heat. Drizzle a scant 1 teaspoon olive oil on top for shine, and scatter a small extra dusting of grated Parmesan.

Serve

Serve chilled or at cool room temperature with croutons, sliced baguette, crisp vegetable sticks (celery, carrot, cucumber), or your choice of dippers. Keeps well covered in the refrigerator for up to 4 days—stir before serving.