Place a large pot or casserole on high heat and bring to a boil. Add the asparagus, close the lid and simmer for 7’. You want them just a bit softened but still snappy. Remove to a bowl with ice cold water, drain and keep aside.
For the sauce, place a small pot on medium heat and immediately add the oil along with the spring onions. Cook for 2’ and then add 125ml of water along with half the tarragon, the vinegar and lemon. Bring to a boil and allow to reduce by ⅓. Remove from the heat and pass through a sieve.
Once the mixture has cooled, add it into a medium/small bowl of a food processor with the metal blade attached, along with the avocado, egg yolks the remaining tarragon and the salt. Blitz into a fine cream, just a bit runny and if needed adjust with oil to thicken or water to thinner.
Serve the asparagus and add some of the sauce on their thicker end.