Put the eggs in a large saucepan. Cover with water – at least an inch over the top of the eggs. Cover the pot and bring to a boil over medium-high heat. Once the pot begins to boil, turn the heat off and remove from the heat. Leave the pot covered for 15-20 minutes.
Drain the water. Cover the eggs with ice and fill the pot with cold water to at least an inch over the eggs. Allow eggs to sit for 15 minutes to cool.
Carefully crack the shells and peel the eggshell off. Set the eggs aside, discard the shells.
Cut the eggs lengthwise and remove the yolks, placing the yolks in a medium bowl. Mash the yolks. Add mayo, mustard and vinegar. Mix well. Season with salt and pepper, if desired. Stuff the egg whites with the yolk mixture.
Make the Deviled Eggs no more than TWO days ahead of time. For best results, keep the egg whites and the yolk mixture separate. I like to store the filling in the zip-top bag that I'm going to pipe the filling back into the yolks with. Be sure to keep everything refrigerated until ready to serve.
You can keep these eggs out for a couple of hours at room temperature when you’re ready to serve them. They’re best eaten fresh! After that, you’ll want to store them in the fridge for up to 3-4 days. Use an airtight container!