Break off tough ends of asparagus. Heat 1" of water to boiling in a deep skillet. Add asparagus and cook two minutes to blanch. Drain and transfer asparagus to bowl of ice water to quickly chill. Drain and set aside or wrap and refrigerate until serving.
In a medium bowl, stir together peppers, pecans, and basil.
In a small bowl, whisk together lemon juice, vinegar, mustard, and salt to blend; whisk in oil to make dressing.
To serve, mound salad greens in center of serving platter; arrange asparagus in two clusters on opposite sides of greens. Spoon pecan mixture over greens and asparagus; drizzle dressing over all.