Wash hands with warm, soapy water for 20 seconds.
Place a single layer of eggs in a saucepan. Add enough cool water to rise at least 1 inch above eggs.
Over medium heat, bring water to just boiling. Cover pan and remove from heat.
Let eggs stand about 12-15 minutes.
Run cool water over eggs until cool enough to handle.
Peel eggs, then gently scoop egg yolks into a resealable plastic bag. Add mayonnaise, mustard, salt, and pepper. Seal the bag.
Mash or knead the bag to blend ingredients.
Push mixture toward one corner of the bag. Snip off that corner with scissors. Squeeze yolk mixture into white halves of eggs.
Sprinkle with paprika.