Add the eggs to a saucepan and cover them with cold water until it reaches about half way up their sides, about 1-inch. Place the eggs over high heat and once the water reaches a medium boil (between a simmer and a rolling boil), turn the heat off, cover the saucepan with a lid and set your timer to 8 minutes. This will give you an almost-runny, creamy, bright yellow yolk with whites that are set. Once the time is up, remove the eggs and run cold water over them and peel. Slice the eggs in half, quarter them and then cut those quarters in half, too. Add them to a bowl, along with the mayonnaise, Dijon mustard, a few cracks of freshly ground pepper and a pinch of salt. Gently toss the mixture together, making sure all of the eggs are coated in the mayonnaise mixture.