Start by placing the desired amount of eggs in a pot, in an even layer. Fill the pot with enough cold water to cover the eggs by 2 inches.
Add the vinegar and salt. Place the pot on a stovetop over high heat. Bring water to a rolling boil.
Turn OFF heat, and use a lid to tightly cover the pot. Let the pot sit on the stovetop, covered, for 12 minutes.
Use a slotted spoon to test one egg for doneness. Run the egg under cold water till it's cool enough to handle. Gently crack the shell and peel it off. If it's cooked perfectly (the egg whites will be firm and the yolk will be a pale yellow, and firm), then drain the hot water from the pan and run all the eggs under cold water till they have cooled down. If the eggs need longer, keep them covered for another minute or two.
Keep hard boiled eggs in an airtight container in the fridge until ready to use.