Step 1

Make an anchovy-garlic paste. Mince the anchovies and garlic together until the mixture is mostly smooth and the garlic is almost paste-like, about 3 minutes; set aside.

Step 2

Whisk the egg yolks. Place the egg yolks in a medium bowl and whisk until smooth.

Step 3

Add the mustard. Whisk in the mustard until just combined.

Step 4

Add the anchovy-garlic paste. Whisk in the anchovy-garlic mixture.

Step 5

Whisk in the lemon juice. While whisking, pour in the lemon juice, then whisk until smooth.

Step 6

Whisk in the olive oil. While whisking, slowly pour in the olive oil to create a thick emulsion. Once all of the olive oil is added, whisk for another minute to thicken.

Step 7

Finish with vegetable oil. Continue whisking and slowly pour in the vegetable oil. Again, once all of the vegetable oil is added, whisk for another minute to thicken.

Step 8

Season and serve. Whisk in the Parmesan cheese. Taste and season with black pepper as needed. Serve immediately.