Chop together anchovy fillets, garlic, and pinch of salt. Use the side of a knife blade to mash into a paste, then scrape into a medium bowl. Whisk in egg yolks, 2 Tbsp. lemon juice, and mustard. Adding drop by drop to start, gradually whisk in olive oil, then vegetable oil; whisk until dressing is thick and glossy. Whisk in Parmesan. Season with salt, pepper, and more lemon juice, if desired.