1. Steam the asparagus over plenty of boiling water for 3-5 mins, depending on the thickness of the spears.
2. Bring a pan of salted water to the boil and add the vinegar. Whisk to make a whirlpool. Once if s settled, crack an egg in the middle. Simmer for 2-3 mins, remove and keep warm. Repeat with the other eggs.
3. Melt the butter in a pan and stir in the lemon juice and tarragon. Pile the spears of asparagus on to each toasted brioche. Top with a poached egg and spoon on the butter sauce.