Using a vegetable peeler, shave off the skin from the bottom 3 inches or so of each asparagus stalk, so they cook evenly. Snap off the hard stubs at the bottom—they’ll break naturally at the right point as you bend the bottom of the asparagus. To prepare the scallions, trim the roots and the wilted ends of the green leaves. Peel off the loose layers at the white end, so the scallions are all tight, trim, and about 6-inches long.

Bring one quart of water (or enough to cover the vegetables) to a boil in a wide deep skillet, and add the asparagus and scallions. Adjust the heat to maintain a bubbling boil and poach the vegetables, uncovered, for about 6 minutes, or more, until they are tender but not falling apart and cooked through but not mushy. To check doneness, pick up an asparagus spear by its middle with tongs: it should be a little droopy, but not collapsing.

As soon as they are done, lift out the vegetables with tongs and lay them in a colander (any fat asparagus spears may take a little longer so leave them in a few minutes more). Hold the colander under cold running water to stop the cooking. Drain briefly, then spread on kitchen towels and pat dry, and sprinkle with about ½ teaspoon salt over them.

Slice the asparagus and the scallions into 1-inch lengths and pile them loosely in a mixing bowl. Drizzle the oil and vinegar over the top, and sprinkle on the remaining salt and several grinds of black pepper. Toss well, but don’t break up the vegetables. Quarter the eggs into wedges and slice each wedge into 2 or 3 pieces; scatter these in the bowl and fold in with the vegetables. Taste and adjust the dressing. Chill the salad briefly, then arrange it on a serving platter or on salad plates.