Add the salt to 6 qt. of water and bring to a boil. Cook the pasta until not quite al dente. Drain, reserving 1 3/4 cups water.
Meanwhile, thoroughly whisk eggs and yolks together. Stir in half of the cheese and season with pepper.
Heat the oil in a large pot over medium. Cook guanciale until crisp around the edges, 7-10 minutes. Remove from heat and transfer guanciale to a separate container. Pour out fat, returning 3 Tbsp. to the pot.
Add 1 cup of the reserved water to the pot with the fat. Bring to a boil and add the pasta.
Whisk 1/4 cup of the remaining water into the egg mixture. Slowly add the pasta, stirring constantly, until cheese has melted and the egg has thickened to form a glossy sauce. Thin with the remaining water until creamy.
Mix in guanciale and serve, topped with additional black pepper and remaining cheese.