Bring a pot of water to a boil. Carefully lower eggs into the pot and cover. Reduce the heat to a simmer and boil for 10 minutes.
Meanwhile, slice tomato and cut avocado.
Prepare an ice bath. When eggs are done, immediately place in ice bath and allow to cool down.
Peel eggs and separate the yolks from the whites. Chop the egg whites and set aside.
Place egg yolks, avocado, dijon mustard and white pepper in a bowl. Mix until creamy.
Stir in chopped egg whites. Season to taste with salt and pepper.
Spread egg salad on a slice of bread, then top with tomato slices and then the second slice of bread. Cut in halves and enjoy!