To Make the Dressing:

1. Combine anchovy fillets, minced garlic, egg yolk or mayonnaise, lemon juice, mustard, Worcestershire sauce, salt, and olive oil in a food processor and process until blended well. 
2. With the food processor on, slowly add the olive oil and then the vegetable oil in a thin stream, and continue to process until thoroughly emulsified.
3. Transfer to a bowl and whisk in grated Parmesan cheese and black pepper to taste. Taste to see if you want to add more black pepper, salt, or lemon juice. If it’s too acidic for you, you can add a little more extra virgin olive oil. Set aside.

To Make the Croutons:

1. Preheat the oven to 375°F.
2. Toss bread pieces with olive oil and arrange in a single layer on a baking sheet.
3. Sprinkle with salt and pepper, and toss to coat.
4. Bake for 10-15 minutes, tossing every 5 minutes, until golden brown on all sides. Remove from the oven and cool on the pan.

To Make the Salad:

1. Remove any tough outer leaves from the hearts of romaine and discard. Gently tear the remaining inner, more tender leaves into large bite-sized pieces. Place in a large wooden salad bowl or your choice of serving bowl.
2. Shave the Parmesan with a vegetable peeler to create thin slivers.
3. Gently toss the lettuce, croutons, and dressing together in the bowl. Garnish generously with shaved Parmesan cheese and serve immediately.