Add all ingredients to a blender or food processor and blend until smooth. Taste and add salt if needed. For a thinner dressing, stir in milk 1 teaspoon at a time.
Let sit in the fridge for 15–20 minutes before using so the flavors can meld.
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Notes
Note 1: Anchovy paste is usually found in a tube near the condiments or canned fish. If you skip it, the dressing will lose some depth. Add a little extra salt to make up for it.Note 2: For the best flavor and salad dressing texture, use a block of Parmesan and grate it with a zester/microplane. If using pre-grated cheese (which is more tightly packed), start with 3 tablespoons and adjust as needed.Storage: Store in a sealed jar in the fridge for up to 1 week. Stir or shake before using—separation is normal.