For the asparagus, drizzle the asparagus with the olive oil and heat a griddle pan until very hot. Place the asparagus into the griddle pan and season well with salt and freshly ground black pepper. Cook, turning frequently for 5-6 minutes, until tender and striped with griddle marks.
For the hollandaise, blend the egg yolks, mustard and lemon juice together in a jug with a hand-held blender. With the blender still running, gradually pour in the melted butter, until the hollandaise reaches the consistency of a loose mayonnaise.
Serve the asparagus lined up on a plate with the fried or poached egg placed on top. Spoon the hollandaise around the side and garnish with chopped chives.