Begin by bringing a large pot of salted water to a boil. Add spaghetti or rigatoni and cook until al dente, reserving 1 cup of pasta water before draining.

In a non-stick pan, heat olive oil over medium heat. Add anchovies and cook, stirring, until they dissolve into the oil.

In a bowl, whisk together eggs and grated Pecorino Romano until creamy; set aside.

Remove the pan from heat, add drained pasta, pour in the egg mixture, and mix. Gradually add reserved pasta water until the sauce is creamy.

Serve immediately, garnishing with extra Pecorino Romano and cracked black pepper.