Preheat the oven to 180C/350F/Gas 4.
Toss the asparagus, olive oil, salt and freshly ground black pepper together in a bowl, then place onto a baking sheet and roast in the oven for ten minutes, or until the asparagus is tender.
Transfer the asparagus to a bowl and add the chopped herbs and a drizzle of olive oil. Stir well to coat, then spoon onto a serving plate and scatter over the grated cheese.
For the new potatoes, melt the butter and oil in a frying pan, add the potatoes, season with salt and freshly ground black pepper and fry for 3-4 minutes, or until golden-brown on all sides.
For the poached egg, fill a small pan with boiling water and add the vinegar. When the water is gently simmering, swirl the water to make a whirlpool, crack the egg into the centre of the whirlpool and leave to cook for 3-4 minutes, or until the white has just set. Remove with a slotted spoon.
To serve, pile the fried new potatoes on the serving plate next to the asparagus and top with the poached egg.