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1. Add water to a large saucepan to a depth of 1 inch; set a large vegetable steamer in pan. Bring water to a boil over medium-high heat. Add eggs to steamer. Cover and steam eggs 16 minutes. Remove from heat. Place eggs in a large ice water-filled bowl.
2. While eggs cook, combine 3 tablespoons water, vinegar, and sugar in a medium microwave-safe bowl; microwave at HIGH 2 minutes or until boiling. Add celery; let stand 15 minutes. Drain.
3. Meanwhile, combine avocado, mayonnaise, juice, mustard, pepper, and salt in a medium bowl, stirring well until smooth.
4. Peel eggs; discard shells. Slice eggs in half lengthwise; reserve 2 yolks for another use. Chop remaining eggs and egg whites. Gently stir eggs, celery, and sunflower seeds into avocado mixture. Top 4 bread slices with about 1/2 cup egg mixture, 1/4 cup arugula, 1 tomato slice, and remaining 4 bread slices.
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