Bring a large pot of salted water to a boil. Fill a large bowl with water and a few handfuls of ice cubes. Snap off the ends of the asparagus – they will naturally break where the stalk transitions from woody to tender. Wash thoroughly or give the stalks a good soak. Cut into two-inch pieces. When the water is boiling, add the asparagus. Cook for two minutes – just until tender. Use a slotted spoon to remove them from the pot; transfer to the ice bath. Let the pot of water continue boiling as you prepare the rest of the dish.
To make the sauce: in a food processor or with an immersion blender, purée the asparagus stalks (save the tip pieces for garnish) with four tablespoons of olive oil until completely smooth.
Finely chop the spring onions into ¼-inch pieces. Heat two tablespoons of olive oil in a sauté pan over medium heat. At this point, pour the pasta into the boiling water. Add the scallions to the sauté pan and season with salt and pepper. Sauté for a few minutes; then add the asparagus tips. Drain the pasta and add to the sautéing mixture, along with the asparagus sauce. Let the pasta cook for one minute more; then serve garnished with the chopped parsley.