First, prepare the asparagus. Cut the tips off and reserve. The remainder of the asparagus spear should be cut into thin rounds (¼ inch or even less). Fill a medium saucepot with water and bring to a boil. Have a bowl of ice water ready to shock the asparagus. When the water boils, add a tablespoon of salt, and stir. Add the asparagus tips for about 10 seconds then add the rest of the asparagus pieces for another 30 seconds. Remove or strain through a colander all the asparagus and immediately put them into the ice bath. Once they have cooled down, remove the asparagus and dry on paper towels. Set aside.

In a skillet over medium heat, add the olive oil and cook the guanciale until it becomes somewhat crispy (5-10 minutes). Remove with a slotted spoon to paper towels to drain excess fat.

While your guanciale browns, fill a large pot with water and bring to a boil. Use less water than you normally would to make a pound of pasta (about 3 quarts). Salt the water with about 2 tablespoon of kosher salt.

In a large mixing bowl, add the crisped guanciale, egg yolks, cheese and pepper and mix thoroughly. Add the asparagus to this mixture. Set aside.

Add the spaghetti to the pot and cook until al-dente. Move the spaghetti directly from the pot to the large mixing bowl and stir for about 20 seconds. If you need more creaminess and sauce, add a little of the pasta water to the bowl. Serve immediately with extra grated cheese on top.