Make the carbonara sauce. In a bowl, whisk together the egg yolks, parsley, cheese, salt and pepper. Set aside.
Lay the bacon strips in a cold frying pan (starting in a cold pan will prevent smoking).
Bring the pan up to medium high heat and fry until crisp. Remove strips from heat and drain on paper towels.
Reserve 2 tablespoons of bacon grease and drain the rest. Add the asparagus spears to the pan and saute until crisp tender, about 4-5 minutes. Remove from heat.
Bring a large pot of water to a boil. Add a generous handful of salt to the water, then add in the spaghetti. Boil until al dente or according to the package instructions.
Reserve 1 cup of pasta water, and set aside. Then drain the pasta and return it quickly to the pot to keep the heat.
Slowly stream in about 1/3 cup of pasta water into the carbonara sauce, whisking the entire time. Whisk until the sauce is smooth and creamy.
Pour the sauce over the hot spaghetti and toss quickly to combine. Keep tossing until the sauce becomes glossy and coats the spaghetti. Add some more pasta water if it seems too thick.
Plate the spaghetti immediately and top with a few bacon strips and asparagus.