Preheat the oven to 450°F/230°C/gas 8.

Toss the broccolini in a large bowl with the 2 tsp of oil and a big pinch of salt and a smaller pinch of pepper. Spread out on a rimmed baking sheet and roast, turning once or twice, until the stalks are just tender but still firm and the florets are lightly charred, 5 to 7 min­utes. Let the broccolini cool while you make the dressing.

Whirl the lemon juice and zest, vinegar, honey, mustard, egg yolk, and a big pinch of salt in a blender until smooth. With the blender running, slowly drizzle in the remain­ing 1/2 cup/120 ml of oil through the hole in the lid and process until smooth and silky. Taste and add more salt as needed.

When the broccolini is cooled to room tem­perature (or it can still be a just a little warm), transfer it to a large bowl and add the avo­cado, pistachios, and chives. Toss with enough of the dressing to coat well (reserve any extra dressing for another use). Divide the salad between four plates. Put the parsley on a small plate and, one at a time, roll the eggs in it to coat thoroughly. Put an egg on top of each salad and garnish with freshly ground pepper. For a dramatic presentation, cut a small slit in the side of each egg to let the yolk begin to flow out just before serving.