1. Place the eggs in a saucepot and cover with cold water by 1-inch. Place over medium heat. Let the eggs come to a gentle simmer. Once the water comes to a simmer, and just before it begins to boil, cover the pot and turn off the heat. Set a timer for 10 minutes.
2. Fill a large bowl with lots of ice and some water.
3. When the timer goes off, carefully pour out the hot water and place the eggs in the ice bath until cooled completely, about 5 minutes. Then peel the eggs.
4. Slice the eggs in half and press on the bottoms of the halves with your thumb, popping out the yolks into a bowl. Set the whites aside for a moment.
5. Mash the yolks with the tines of a fork, and then add the mayonnaise, mustard and relish. Stir together until smooth and creamy, and then season with salt and pepper.
6. Chop up the whites of the eggs and add them to the bowl along with dill, celery, lemon zest and shallots. Stir, taste and adjust the seasoning to your liking.
7. Lightly toast the bread, and then generously butter each slice. Cut each slice in half on the diagonal into triangles and top with a nice pile of egg salad (about 2 heaping tablespoons).