Mound anchovies, garlic, and salt on a cutting board. Using the side of a chef’s knife, mash and chop until well combined, then continue to work mixture, holding knife blade at an angle, until a smooth paste forms. (Alternately, you can use a mortar and pestle or mini chopper to do this step.)

Whisk egg yolk, lemon juice, and mustard in a medium bowl. Place a kitchen towel in a medium saucepan, then place bowl in pan. (This holds the bowl in place while you whisk with one hand and pour oil with the other.)

Adding drop by drop to start and whisking constantly, drizzle a few drops of oil into yolk mixture. Continue, going slowly, until mixture looks slightly thickened and glossy. Continue to whisk, gradually adding oil in a slow, steady stream until all oil has been used and mixture looks like mayonnaise. Add a dash of water and whisk, adjusting with more water if needed, until dressing is the consistency of heavy cream. Add anchovy mixture and Parmesan and whisk until smooth. Taste and adjust seasoning with salt, if needed.