Begin by making the gnocchi: Prick potatoes all over with a fork, and bake them in a 425 degree oven, directly on the rack, for forty minutes, or until tender when tested with a fork.
When the potatoes are done baking, scoop them out of their shells and rice them into a large bowl. Add the cheeses, eggs, and salt. Stir gently together. Add the flour, and as gently as possible, knead the dough into a ball.
Remove a golf ball sized piece of dough, and on a floured board, roll into a thin log, about a half inch thick. Cut the log into ¾ inch pieces. Place them on a floured parchment lined pan. Repeat until all the dough is used up. You will only need half the gnocchi for this recipe. You can freeze the rest of the gnocchi by placing the sheet full of them in the freezer. When they're frozen, you can put them in a freezer bag to store them.
Boil a large pot of salted water. Drop a quarter of the gnocchi at a time. Using a slotted spoon, remove the gnocchi as soon as they rise to the top. Drop them into a colander as soon as they're done so they dry completely. Repeat until all the gnocchi are cooked. You'll only need half the gnocchi for this sauce. Save the rest for another use. Check out this site for lots of other gnocchi sauce recipes.
Also, cook the asparagus: Bring one inch of water to a boil in a three quart saucepan. Add the asparagus and simmer, covered, for 5 minutes. Drain well.
And, make the pesto: Place all the ingredients, except the oil, in the food processor. Pulse until everything is ground up. With the motor running, stream in the olive oil. Toss the gnocchi and asparagus with the pesto.
Serve garnished with basil and the shaved Parmesan cheese.