Bring a large pot of water to a boil and gently add the eggs. Set a timer for 8 minutes. While the eggs are boiling, prepare a large ice water bath in a large bowl. After 8 minutes, remove the eggs from the boiling water with a slotted spoon and set the eggs in the water bath for 5 minutes.
While the eggs are in the water bath, prepare the egg salad sauce. Add the Greek yogurt, mayonnaise, mustards, vinegar, salt, pepper, paprika, and hot sauce to a bowl and mix until well combined. Set aside.
Peel the eggs and chop the eggs into small pieces. Add the eggs to the sauce and mix until combined. Cover and refrigerate for at least 30 minutes.
Toast the bread and assemble the egg salad sandwiches. Place the lettuce you are using on top of a piece of toast (good for keeping the bread from getting soggy). Then, layer the celery, tomato, onion, and pickles in top of the lettuce. Scoop ⅓ cup of egg salad on top of the ingredients and season with fresh dill.
Add the last piece of bread to the top of the ingredients and enjoy.