Place the Greek yogurt, grated Parmesan cheese, lemon juice, olive oil, Dijon mustard, and Worcestershire sauce in a medium mixing bowl.
Add the minced garlic and anchovy paste to the mixture.
Whisk all ingredients vigorously until the texture is smooth and the oil is fully emulsified into the yogurt.
Season with kosher salt and freshly ground black pepper, whisking again to incorporate.
Transfer the dressing to a sealed container and refrigerate for at least 15 minutes to allow flavors to develop.
Store in the refrigerator for up to 5 days and stir well before each use.