Bring a large pot of salted water to a boil. Add asparagus and cook for about 10 minutes, until asparagus is tender and juicy. Remove asparagus from water with a small (spider) strainer and cool.
Keep water boiling and add the pasta. Cook until tender, about 10 minutes, or whatever the time listed on the package. Reserve a cup of pasta water, then drain the pasta, set aside.
If making poached eggs, bring a saucepan of salted water to a simmer. Crack each egg into a small bowl or measuring cup, fill 2-3 extra bowls with ice cold water.
Cooking one at a time, stir water with a spoon until it’s spinning around and quickly place the bowl close to the surface of the water and slip the egg into the the center of the pot. Cook undisturbed for 4-5 minutes, until you see the egg white turn from translucent to white, but the yolk should remain soft and runny. Gently remove the egg from the water with a slotted spoon and transfer it to a bowl filled with cold water. This will stop the egg from cooking further, but give you enough time to poach the other egg and make the sauce. You can also cook 2-3 eggs at the same time, if your pot is big enough.