Place yogurt in a medium bowl with, dijonnaise, lemon juice, avocado (if using) and dill and mash together with a fork. Mash until creamy throughout.
Season with salt and fresh cracked pepper to taste.
Chop eggs and stir them gently in the yogurt mixture.
Set aside in refrigerator.
Slice the cucumber horizontally so that you make large round coins about 1/4-1/2 inch thick. Slice the radishes horizontally so that you make round coins about 1/4-1/2 inch thick.
Place four cucumber “coins” on a plate and four radish “coins” on the plate. Top them with 1/4 cup egg salad. Add a tomato slice to the cucumber coin sandwiches and add a sprinkle of fresh cracked pepper and cover with a cucumber coin. Cover radish sandwiches with a radish coin, if desired.