Boil 4 quarts of water in a medium pot over high heat. Put the eggs in gently, straight from the refrigerator, and boil on high for 60 seconds, turn down the heat so that the water is at a gentle simmer, cover, and cook for 12 minutes. Take the eggs directly from the pot and plunge into cold water, preferably with a few ice cubes. Allow the eggs to cool in the water for 30 minutes.
While the eggs are cooling, mix together the mayonnaise, mustard, and salt. Roughly chop the cooled eggs and fold into the mayo-mustard mixture. If you stir it just until incorporated you’ll have a coarse, firm egg salad where the egg parts are clearly defined. If you keep stirring, you’ll have a creamier, more uniform egg salad. You do you.
Serve on crackers, biscuits, bread, etc.