1. Preheat oven to 450°.
2. Place asparagus on a jelly-roll pan. Drizzle with 2 teaspoons oil; sprinkle with 1/4 teaspoon pepper and 1/8 teaspoon salt. Toss gently to coat; arrange in a single layer. Bake at 450° for 5 minutes or until crisp-tender.
3. 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 one-fourth of the asparagus.
4. Add water to a large skillet, filling two-thirds full; bring to a boil. Reduce heat; simmer. Add vinegar. Break each egg into a custard cup, and pour each gently into pan; cook 3 minutes or until desired degree of doneness. Carefully remove eggs from pan using a slotted spoon; place 1 poached egg on each salad. Sprinkle with remaining 1/8 teaspoon pepper. Arrange 2 bread halves on each serving.