Whisk together eggs and Pecorino Romano in a medium bowl.
Cook pancetta in a large skillet over medium heat, stirring often, until evenly browned, about 10 minutes.
Meanwhile, bring a large pot of salted water to a boil. Cook spaghetti according to package directions, reserving 2⁄3 cup pasta cooking water. Drain; add spaghetti to pancetta in skillet. Remove skillet from heat.
Stir 1⁄4 cup pasta water into egg mixture to temper eggs. Add egg mixture to spaghetti in skillet; stir constantly, adding enough pasta cooking water to reach desired consistency, until spaghetti is coated and eggs are just set but not curdled. Garnish with black pepper and/or additional Pecorino Romano. Note: Guanciale is the traditional cured pork choice for carbonara. It has a high fat-to-meat ratio, which contributes to a silky end product. But it can be hard to find and expensive. So use pancetta instead. Bacon can be used in a pinch, too. Pecorino Romano is aged sheep’s-milk cheese with a sharp and salty flavor. For the best texture, grate your own. But you can substitute Parmesan, no problem.