First, hard boil the egg. You can do this in your preferred method, or else use the following. Bring a small pot of water to a boil and add the egg. Cook for 9 minutes at a simmer, then transfer the egg to a bowl with iced water. Let it cool in the water, then peel.
While the egg is cooking, trim the ends from the asparagus, either cutting above any purple/grey part or snapping where it naturally breaks.
I tend to re-use the water from the egg for the asparagus, if the pot is big enough, or else use a separate pot. Add a pinch of salt to the water, add the asparagus, cover and bring back to a simmer. Cook for around 2 - 3 minutes until it is just tender then transfer to a bowl of iced water (this helps preserve the green color). You can leave in a few minutes if you prefer it cool, or else just place in water around 30 seconds and remove to a plate to be warm.
As the asparagus is cooking, mix together the vinaigrette ingredients (oil, lemon, mustard and shallot) ad whisk together to emulsify.
Place the asparagus on a plate (or plates) and drizzle over the vinaigrette. If you like, toss the asparagus in it slightly. Then place the egg in a small sieve and press through with the back of a spoon to form a crumb-like egg topping over the asparagus.