Place eggs in a single layer in a saucepan and cover with water. Bring to a boil, then simmer for 9–10 minutes. Rinse under cold water to stop the cooking and cool them quickly.
Peel the eggs gently. Slice in half lengthwise and scoop yolks into a bowl. Mash the yolks with a fork until smooth.
Stir in mayonnaise, mustard, vinegar or lemon juice, and a pinch of salt and pepper. Mix until creamy and scoopable. Taste and adjust if needed—you’re aiming for a gentle tang, not a splashy punchline.
Fill or pipe the yolk mixture back into the egg whites. If you’re not fancy with a piping bag, a spoon works just fine.
Sprinkle with paprika and any optional mix-ins you love. Chill for at least 15 minutes for best flavor, or serve right away if you’re sprinting to the party.