1Prepare an ice water bath by filling a large bowl halfway with ice and water; set aside.
2Set the egg in a medium pot and fill it two-thirds of the way with cold water. Bring to a boil, then remove from heat. Cover and let sit for 10 minutes.
3Using a slotted spoon, transfer the egg to the ice water bath. (Reserve the hot water for cooking the asparagus.) Crack the egg against the bowl in the water bath so that the shell fills with water. Peel while still warm. Keep the egg in the water until cool. Set the ice water bath aside, adding more ice as needed.
4Bring the pot of hot water back to a boil and salt heavily. Add the asparagus and cook until the stalks are knife tender, about 2 to 5 minutes depending on their thickness. Drain and transfer immediately to the ice water bath to cool. Once cool, dry with a paper towel and set on a serving dish.
5In a small, nonreactive bowl, whisk together the lemon juice, mustard, and a pinch each of salt and pepper. Add the oil in a slow, steady stream while whisking. Season as needed with more salt and pepper and drizzle the vinaigrette over the asparagus.
6Using the back of a metal spoon, push the reserved hard-boiled egg through a strainer and sprinkle over the asparagus. Season the egg with salt and pepper and serve.