Combine first 7 ingredients in a small bowl, stirring with a whisk. Gradually add olive oil, stirring well with a whisk.
Steam asparagus, covered, for 3 minutes.
Drain and rinse under cold water; drain. Arrange 2 prosciutto slices in the center of each of 4 plates. Arrange asparagus spears evenly over prosciutto.
Add water to a large skillet, filling two-thirds full; bring to a boil. Reduce heat; simmer. Break eggs into each of 4 (6-ounce) custard cups coated with cooking spray.
Place custard cups in simmering water in pan. Cover pan; cook 10 minutes.
Remove custard cups from water, and carefully remove eggs from cups. Arrange 1 egg over each serving, and drizzle with about 1 tablespoon dressing.
Sprinkle each serving with 1 teaspoon chives, if desired.