Put 1 large and 1 smaller pan of water on to boil. Scrub the potatoes and cut them into 1cm-thick slices. When the large pan of water is boiling, add a pinch of salt and the potatoes. Simmer for 12-15 mins till tender when pressed with the tip of a knife.
When the small pan boils, carefully add the whole eggs. Simmer for 7 mins (8 for firmer yolks). Lift the eggs out and plunge into a bowl of cold water. Set aside.
Meanwhile, snap the ends off the asparagus (the spears will break at the right point when bent). Trim the roots and any ragged greens off the spring onions. Halve them widthways to make 8 pieces. Halve each piece lengthways to make 16 short lengths. Finely chop the chives.
Finely grate some zest off the lemon and set aside. Juice half the lemon into a small bowl. Add 1 tsp each sugar and horseradish mustard (keep the rest for later). Add 1 tbsp olive oil. Peel and crush the garlic and add that with a pinch of salt and pepper. Whisk together to make a dressing. Taste and add more salt, pepper, sugar or horseradish mustard if you think it needs it.
Warm a dry griddle or frying pan over a medium heat for 2 mins. Add the asparagus and spring onions. Cook for 4-5 mins, turning the veg a few times, till a little charred and tender.
The potatoes should be tender and cooked through by now. Drain and tip them back into the pan. Add half the dressing and toss to mix. Arrange on 2 plates. Add the asparagus and spring onions to the plates.
Drain the eggs. Peel, halve and nestle them in the salads. Scatter over the chives and lemon zest. Drizzle over the remaining dressing and serve.