Preheat oven to 375°F (190°C). Spread the bread cubes on a baking sheet. Drizzle 2 tablespoons olive oil over the bread, sprinkle the minced garlic, 1 teaspoon salt and 1 teaspoon freshly ground black pepper. Toss to coat. Bake for 8–12 minutes, tossing once halfway through, until golden and crisp. Let cool slightly, then pulse 6–8 times in a food processor until coarse crumbs form. Set aside to cool completely.

Caesar Dressing

Emulsify dressing

In a medium bowl or shallow jar, mash the anchovy fillets and minced garlic into a paste with the back of a spoon or a microplane. Add the Dijon mustard, lemon juice, white wine vinegar and Worcestershire sauce and whisk to combine.

Add the egg yolk (or 1 tablespoon mayonnaise) and whisk thoroughly until incorporated. While whisking constantly, drizzle in the extra-virgin olive oil and neutral oil in a thin, steady stream to form an emulsion. The dressing should thicken slightly.

Stir in the 2 tablespoons grated Parmesan, then season with 1 teaspoon salt and 1/2 teaspoon freshly ground black pepper. Taste and adjust acidity with more lemon juice or salt if needed. If dressing is too thick, whisk in up to 1 tablespoon cold water to reach desired consistency. Refrigerate until ready to use (up to 24 hours).

Salad Assembly

Toss and serve

In a large mixing bowl, combine the arugula and chopped romaine. Add about two-thirds of the dressing (start with 3–4 tablespoons) and toss gently but thoroughly until leaves are evenly coated. Add more dressing to taste, but avoid overdressing—the salad should be lightly but evenly dressed.

Add the freshly grated Parmesan and toss once more. Scatter the made-in breadcrumbs over the salad and toss gently to distribute. If using, top with sliced grilled chicken and extra shaved Parmesan.

Divide among 4 plates, garnish with lemon wedges and serve immediately so breadcrumbs remain crisp.