Trim or snap tough bottom ends off the asparagus spears. With a peeler, peel the bottom portion of each of the spears.
Put the asparagus in a large skillet. Add enough water to cover. Bring to a boil. Reduce to a simmer and cook until spears are just tender, about 5 to 7 minutes. Drain and keep warm.
Combine the olive oil, minced anchovy, chopped parsley, shallots, lemon juice, fleur de sel (or Maldon salt) and a pinch of ground white pepper, or to taste.
Drizzle half the dressing over the hard-cooked eggs and lightly toss with a fork. Arrange the asparagus spears on a serving platter. Spoon the egg over the cooked asparagus spears.
Drizzle remaining dressing over the asparagus. Sprinkle chopped parsley over the top to finish.
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