Place asparagus on a jelly-roll pan. Drizzle with 2 teaspoons oil; sprinkle with 1/4 teaspoons pepper and 1/8 teaspoons salt. Toss gently to coat; arrange in a single layer. Bake at 450 degrees for 5 minutes or until crisp-tender.
Place remaining 7 teaspoons oil, 1/8 teaspoon pepper, remaining 1/8 teaspoon salt, shallots, juice, and tarragon in a large bowl; stir well with a whisk. Add arugula; toss gently to coat.
Place about 1 1/2 cups arugula mixture on each of 4 plates. Top each serving with 1/4 of the asparagus.
Add water to a large skillet, filling 2/3 full; bring to a boil. Reduce heat; simmer. Add vinegar.
Break each egg into a custard cup, and pour each gently into the pan; cook 3 minutes or until desired degree of doneness. Carefully remove the eggs from the pan using a slotted spoon. Place 1 poached egg on each salad. Sprinkle with the remaining 1/8 teaspoon pepper. Arrange 2 bread halves on each serving.