Preheat oven to 450°F. Combine broccoli rabe, 1 tablespoon oil, 1 teaspoon salt, and black pepper in a large bowl; toss to coat. Spread in a single layer on 2 rimmed baking sheets, and roast in preheated oven until stalks are just tender but still firm and the florets and leaves are lightly charred, 9 to 10 minutes, rotating pans halfway through roasting time. Let cool while you make the dressing.

Fill a bowl with ice water, and set near the stove. Bring a medium pot of water to a boil over high. Reduce heat to maintain a gentle simmer, and slowly lower eggs into water using a slotted spoon. Cook 5 minutes. Remove eggs, and plunge into the ice bath briefly to stop the cooking process. Working with 1 egg at a time, cradle an egg in your hand, and gently tap the shell with the back of a spoon to make tiny cracks all over like a mosaic. Peel eggs under running water beginning at the thickest end. Let eggs stand at room temperature.

Combine egg yolk, lemon zest and juice, vinegar, honey, mustard, and remaining 1 ½ teaspoons salt in a blender, and process until smooth. With blender running, slowly drizzle in remaining ½ cup oil through hole in lid, and process until smooth and silky.

When broccoli rabe is slightly cooled but still just a little warm, transfer it to a large bowl, and add avocado, pistachios, and chives. Toss with enough of the dressing to coat well; reserve any extra dressing for another use. Divide salad among 4 plates. Place parsley on a small plate, and roll eggs in it to coat thoroughly. Place an egg on top of each salad. 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.