Step 1

Gently lower eggs into a medium pot of boiling water; cook 6 minutes. Transfer eggs to a bowl of ice water and let cool.

Step 2

Heat a dry large cast-iron skillet over medium-high until smoking hot. Cook leeks, cut side down, pressing to ensure contact with skillet, until blackened, about 5 minutes. Reduce heat to medium; add butter and rotate skillet to evenly coat leeks. Transfer leeks to a platter with a slotted spoon.

Step 3

Add asparagus to skillet, season with kosher salt and pepper, and cook, tossing occasionally, until bright green and crisp-tender, about 4 minutes. Remove from heat, add lemon juice and mustard, and toss asparagus to coat. Transfer to platter with leeks and spoon sauce over.

Step 4

Peel eggs, halve, and place on top of vegetables. Top with sea salt.