Wash and peel the white asparagus, cut off the woody ends and cut into pieces. Cook in 1/2 litre salt water with some sugar for about 20 minutes. Wash green asparagus, cut off woody ends.
Cut the asparagus into pieces. Add to the white asparagus after 10 minutes. Wash the tarragon. Pluck leaves. Rub the fillet with salt and pepper. Heat oil. Brown the meat well in it. Then fry over medium heat for 10-15 minutes.
Drain the asparagus. Measure out 1/4 litre of asparagus water. Heat the fat. Sweat flour in it. Deglaze with cream and asparagus water and boil up. Whisk milk and egg yolk, stir in. Do not boil any more.
Season to taste with salt, pepper and mustard. Add asparagus and tarragon to the sauce. Serve everything. Garnish with tarragon.