Fill a large frying pan or skillet, large enough to hold the asparagus, two-thirds full with water and bring to a boil. Add 3 tablespoons salt and the asparagus. Cover the pan to return the water to a boil, then cook, uncovered, until the asparagus spears and tender but still bright green, about 7 minutes. Drain and set on a kitchen towel or paper towel to dry.
Fill a medium saucepan half-full with water and bring to a simmer. In a medium, heat-proof bowl, combine the eggs, lemon juice, and salt and pepper to taste and whisk until the mixture is pale. Slowly whisk in the oil to emulsify. Place the bowl over the simmering water and, whisking constantly, cook the sauce over the water bath until it thickens.
Serve the asparagus spears and sauce so that guests may dip the spears in the sauce and eat with finger.