Cook pasta according to the package directions. Drain, reserving ½ cup of the cooking water, and return pasta to the pot.
Meanwhile, cook bacon in a nonstick or cast-iron skillet over medium heat until crisp, 6 to 8 minutes. Transfer to a paper towel-lined plate. Crumble when cool.
Wipe out the skillet and return it to medium heat. Crack eggs into it and cook until whites are set but yolks are still runny, 3 to 4 minutes.
Toss pasta with bacon, reserved pasta water, ½ cup of the Parmesan, ½ teaspoon salt, and ¼ teaspoon pepper.
Divide pasta among bowls and top with eggs. Sprinkle with remaining 2 tablespoons of Parmesan.