Place the 6 large eggs in a single layer at the bottom of a saucepan. Cover with cold water about an inch above the eggs. Bring to a boil over medium-high heat.
Once boiling, cover the saucepan with a lid and remove from heat. Let eggs sit for 10-12 minutes to cook through.
Drain hot water and transfer eggs to a bowl of ice water. Cool for at least 5 minutes to make peeling easier.
Gently tap each egg on a hard surface and peel off the shell. Rinse any small shell pieces under cold water.
Slice each egg in half lengthwise and carefully remove yolks into a medium bowl. Arrange egg whites on a serving platter.
Mash yolks with a fork until smooth. Add mayonnaise, zucchini relish, and Dijon mustard. Mix until creamy and well combined. Season with salt and pepper to taste.
Fill each egg white half with the yolk mixture using a spoon or piping bag, being generous to pack each bite with flavor.
Sprinkle paprika on top for color and a hint of smoky flavor. Serve and enjoy.