Boil the eggs: Place the eggs in a pot and cover them with cold water by an inch. Bring to a gentle boil over medium-high heat, then cover and turn off the heat. Let the eggs sit for 11 to 12 minutes.

Chill the eggs: Transfer the eggs to an ice bath and chill for at least 10 minutes.

Peel the eggs: Gently crack the shells and peel under a thin stream of water to reduce any sticking.

Prepare the filling: Slice the eggs lengthwise; pop the yolks into a bowl. Mash the yolks until smooth and blend in mayonnaise, Dijon mustard, vinegar or lemon juice, salt, and pepper. Adjust seasonings to taste.

Spoon or pipe the filling: Spoon the mixture back into the egg whites or use a zip-top bag to pipe in the filling.

Garnish: Dust with paprika and add any optional garnishes like chopped chives or dill. Refrigerate until ready to serve.