Bring water to a boil over high heat.
Add the gnocchi and cook until done (just a few minutes - the pasta will rise to the top of the water when it is done.)
As the gnocchi is done, remove it from the hot water with a slotted spoon and place in a large bowl.
Add the asparagus and the shrimp to the boiling water and cook for about 5 minutes or until the shrimp is done.
Using a slotted spoon, remove the asparagus and shrimp from the water and add it to the bowl of gnocchi.
Add pesto a bit at a time to end up with the strength of flavor that you like.