Place eggs in a single layer in a saucepan and cover with enough water that there's 1 1/2 inches of water above the eggs.
Heat on high until water begins to boil, then continue to boil for 9 minutes.
Remove from heat and leave covered for 10 minutes, then rinse under cold water.
Crack egg shells and rise under running water to get all of the shell removed.
Slice the eggs in half lengthwise, removing yolks to a medium bowl, and placing the whites on a serving platter.
Mash the yolks into a fine crumble using a fork. Add mayonnaise, mustard, salt, and pepper, and mix well. Taste to be sure that the mixture is to your liking. (FYI - It is better for the egg mixture to be dry than wet and runny. You can always add more mayo or mustard.)
Place egg mixture in a Ziploc bag and cut a small amount away from one end.
Squeeze egg mixture into each egg white. Sprinkle with paprika and serve.