Fill a pot with water and bring to a boil over high heat. Gently add the eggs to the pot and cook for 8 to 10 minutes, depending on how cooked you prefer the yolks. While the eggs are boiling, prepare a large bowl full of ice water. When the eggs are done, transfer them to the ice water to stop the cooking.
Remove the shell from the eggs and transfer the eggs to a bowl. Use a knife or a fork to break the eggs up into small pieces. Season with salt and pepper, and add the mayo and mustard, and mix well to combine.
Using a small spoon, scoop the seeds out of the 4 slices of cucumber. You can save the seeds for adding to a yogurt dip, juice, or smoothie.
Fill the hollowed cucumber boats with the egg salad. Top with seasoning and parsley, if using.