Oil if you're frying or salted water if you're boiling
Steps:
I'm sure you could make this in a blender, but I didn't want to get a whole blender dirty for this, so I used a mortar and pestle.
Put the pine nuts in a mortar and crush using a pestle. Add the mint, garlic and salt and continue to crush until you have a paste. Add the lemon juice, oil, cheese and pepper, stirring to combine.
For the asparagus, use a sharp knife or mandoline (or a multi-blade knife if you have one) to made noodles out of each spear. If you're using a knife or multi-blade knife, I find it's easiest if you leave the tough bottoms of the stalks attached and use it to hold onto the stalk with one hand using the knife to slice with the other. If you want thinner noodles, just make one set of cuts, then rotate 90 degrees and make another.
You can either boil the asparagus noodles in salted water, or saute them in a little olive oil. Careful not to overcook them as it doesn't take very long. Once cooked, pour a few tablespoons of pesto on top and toss to coat evenly.