1. Make the croutons: Heat the oil in a large skillet or frying pan over medium-high heat until shimmering. Add the bread cubes to the pan, sprinkle with the salt, toss to coat with the oil, and arrange in a single layer. Toast the bread, tossing every minute or so, until the bread cubes are golden-brown on all sides, about 5 minutes total. Remove the pan from the heat. Cool completely.

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

3. Make the dressing base: Whisk the egg yolks together in a medium bowl until smooth. Whisk in the mustard until just combined. Whisk in the anchovy-garlic mixture. While whisking, pour in the lemon juice, then whisk until smooth.

4. Whisk in the oils: While whisking, stream in the olive oil to create a thick emulsion. Once all of the olive oil is added, whisk for another minute to thicken. Continue whisking and slowly stream in the vegetable oil. Again, once all of the vegetable oil is added, whisk for another minute to thicken. Whisk in the Parmesan cheese. Taste and season with black pepper as needed.

5. Prepare the romaine: Cut the romaine into bite-sized pieces and rinse under cool running water. Salad spin to dry or spread the romaine out onto a clean kitchen towel and pat dry.

6. Toss and serve: Place the romaine in a large bowl, add half of the dressing, and toss to combine. Add the croutons and toss again. Add some shaved Parmesan for both garnish and seasoning. Parmesan is salty, so taste and adjust the seasoning with pepper or more dressing as needed after adding the cheese. Serve immediately.

Recipe notes: Store leftover croutons in an airtight container at room temperature for up to one week, or store in the freezer for up to six months. Leftover dressing can be stored in the refrigerator for one day.

(Meghan Splawn is the associate food editor for TheKitchn.com, a nationally known blog for people who love food and home cooking. Submit any comments or questions to editorial@thekitchn.com.)