In large pot, place uncooked eggs in cold water until 1 inch of water covers eggs. Bring to a boil on high heat. Reduce heat to low, cover eggs with a lid, and let simmer for 15 minutes. Remove eggs from heat and run under cold water until cool to the touch. Peel egg shells when cool enough to handle.
Cut boiled eggs half lengthwise. Pop out cooked yolks into a medium size bowl. Mash egg yolks with a fork until crumbly. Add mayonnaise, mustard, and white vinegar to bowl of yolks. Mix well. Set egg halves in containers or on platter before filling. Spoon egg mixture into pastry bag and fill egg halves (a dessert decorator (icing gun) with small star tip works well, or egg halves can be filled using a regular spoon). Garnish with paprika.