Cook the eggs: Place 6 large eggs in the bottom of a large saucepan. Fill with cold water, covering the eggs with about 1 inch of water. Place over high heat and bring to a boil. Reduce heat slightly to medium-high so the water is still boiling, but not too vigorously (to prevent cracked eggs). Boil for about 10 minutes. Transfer the eggs to an ice bath or run under cold water to cool enough to handle.
Peel the eggs, and split them even down the center lengthwise. Carefully remove the egg yolks and set them aside in a small bowl. Give the egg yolks a light mash to break them up slightly.
Add mayonnaise, mustard, vinegar, and salt to the egg yolks. Using a fork, stir and mash the mix until the egg yolks are fully broken up and you're left with a smooth, creamy mixture.
Using a spoon or piping bag with the tip sniped off, scoop / pipe the egg yolk mixture back into the space in the egg whites. Serve as is, top with paprika, or add your own favorite toppings!