1. Heat 1 tablespoon oil in 12-inch nonstick skillet over high heat until beginning to smoke. Add asparagus, 1/4 teaspoon salt, and 1/4 teaspoon pepper; cook until browned and tender-crisp, about 4 minutes, stirring once every minute. Transfer to large plate and cool 5 minutes.
2. Meanwhile, whisk remaining 4 tablespoons oil, vinegar, shallot, cornichons, capers, tarragon, and 1/4 teaspoon pepper in medium bowl until combined. In large bowl, toss mesclun with 2 tablespoons dressing and divide among salad plates. Toss asparagus with remaining dressing and place a portion over mesclun; divide chopped eggs among salads and serve.
STEP BY STEP: Cutting Asparagus on the Bias
1. To cut the asparagus quickly and evenly, arrange the spears in staggered groups of five on a cutting board.
2. Cut them into 1-inch pieces on the bias.