Martha's Favorite Egg Salad Sandwich

INGREDIENTS

• 10 hard-boiled egg whites
• 2 hard-boiled egg yolks
• 2 to 3 tablespoons light mayonnaise
• 1 teaspoon Dijon mustard
• 1 tablespoon freshly squeezed lemon juice
• 1/2 avocado, mashed, plus 1/2 avocado roughly chopped
• Coarse salt and freshly ground pepper
• Boston lettuce, arugula, and tomato slices (optional)
• 12 white sandwich bread, such as Pullman, sliced about 1/2-inch thick, toasted