In a medium skillet, combine oil and breadcrumbs and cook over medium-low heat, stirring occasionally, until toasted and golden brown, 5 to 7 minutes. Add parsley and lemon zest, season lightly with salt, stir to combine, and continue to cook until parsley begins to sizzle and mixture is very fragrant of citrus, 30 seconds to 1 minute. Transfer breadcrumb mixture to small bowl and set aside until ready to serve.

In a large heatproof mixing bowl, whisk together whole eggs and yolks, Parmigiano-Reggiano, Dijon, Worcestershire, and black pepper.

Bring a pot of lightly salted water to a boil. Add pasta and cook, stirring, until al dente.

Meanwhile, in a skillet or saucier, combine olive oil with anchovies and garlic and cook over medium heat, stirring frequently, until anchovies have melted and garlic is lightly golden, about 3 minutes. Measure ½ cup (120ml) pasta cooking water and add to the anchovy-oil mixture.

While whisking constantly, slowly drizzle the anchovy-oil mixture into the egg mixture; take care, because if you add the hot liquid too fast, you may scramble the eggs.

Using tongs and/or a strainer, transfer pasta to egg mixture, stirring it in as you add it to ensure you don't cause the eggs to scramble. Stir well to combine.

Set mixing bowl over pot of boiling pasta water (make sure bottom of bowl does not touch the water) and cook, stirring quickly with tongs, until sauce begins to thicken to a creamy, silky consistency and leaves trails as you stir. Remove from heat, season with salt if needed, and divide into bowls. Serve right away, topping with reserved gremolata breadcrumbs.