Add eggs to saucepan in a single layer; add water to completely cover eggs by about at least an inch. Bring to a boil. Cover and remove from heat. Let stand for 15 minutes.
After 15 minutes drain and fill the saucepan with ice cold water. Let eggs sit in ice water for 10 minutes to cool down then tap each egg firmly on the counter until cracks form and peel under cold running water.
Slice eggs in half lengthwise and remove the yolks.
Mash yolks with mayonnaise and mustard. Add dill relish and a tiny bit of the pickle juice, salt and pepper (optional) and mix well.
Use a spoon or piping bag to add yolk mixture into egg whites.
Garnish with paprika if desired.
Notes
Store any leftovers in the refrigerator in an airtight container for up to 2 days.