Place eggs in a large empty pot. Cover with 8 cups of cold water. Add 1 Tablespoon of vinegar.
Turn heat to high and bring to a boil. Once it starts boiling, turn off heat and cover. Don't remove from the stove - the residual heat helps cook the eggs.
Cook for 13 minutes. At 12 minutes, grab a large bowl and fill with ice water. When eggs are finished cooking, remove eggs 1 or 2 at a time with a slotted spoon and place in ice water.
Let the eggs cool for a minute or two in the ice bath then drain. Dry off the eggs and then peel them, one by one.
Once peeled, slice eggs lengthwise in half. Gently scoop the yolk into a medium sized bowl and place the white egg halves onto a serving platter.
Using a hand mixer, stand mixer, or a whisk - mix the yolks until crumbly and not full yolks. Then, add mayo, yellow mustard, and salt and pepper. Mix until fully combined with no big clumps.
Place egg filling into a piping bag or plastic baggie with the tip cut off to fill the eggs. Fill each egg until filling is gone.
Sprinkle with paprika and enjoy! Eat immediately or place in fridge until ready to serve.