Place the eggs in a medium saucepan and add enough water to cover them by about an inch. Set the pan over medium-high heat and bring the water to a rolling boil. Once boiling, let the eggs cook for 10 minutes. Turn off the heat, cover the pot with a lid, and let the eggs sit in the hot water for another 10 minutes. This ensures they finish cooking gently without becoming overdone.
Carefully drain the hot water from the pot and run cold water over the eggs until they are cool to the touch. For even faster cooling, you can transfer them to an ice water bath and let them sit for about 5 minutes. Once cooled, gently tap each egg on the counter, rolling it slightly to crack the shell. Peel the shell off, making sure to remove any small fragments, then rinse the eggs under cool water to remove any lingering bits of shell.
Using a sharp knife, slice each egg in half lengthwise. Carefully remove the yolks and place them in a medium-sized bowl. Arrange the empty egg whites on a serving platter or plate.
Using a fork, mash the egg yolks until they reach a fine, crumbly texture. Add the mayonnaise and Dijon mustard, stirring until the mixture is smooth and well combined. If needed, add a tiny splash of water or extra mayo to reach the desired creamy consistency. Taste and adjust seasoning if necessary.
To fill the egg whites, you can use a small spoon to scoop the yolk mixture into each egg half. For a neater presentation, I prefer using a piping bag to pipe the mixture into the eggs. This creates a more decorative look while also making the process quicker and less messy.
Place one shrimp on top of each deviled egg, gently pressing it into the filling so it stays in place.
Cover the deviled eggs and refrigerate for at least 30 minutes before serving. Chilling allows the flavors to meld together and helps firm up the filling. Serve cold and enjoy!