Remove the fresh eggs from the refrigerator about a half hour prior to cooking them to allow them to come to room temperature.
Place the eggs in the bottom of a medium saucepan. Add enough cold water to cover one inch above them.
Place the saucepan over medium-high heat and bring the water to a rolling boil.
Boil the eggs for 5 minutes, then turn off the heat and allow the eggs to rest in the water for 20 minutes without a lid.
After 20 minutes, remove the eggs and place them in an ice water bath to stop the cooking process.
Allow the eggs to rest in the ice bath for 10 minutes to cool.
Crack the eggs while in the ice water, and begin to peel them in the water.*If the water is too cold, you can add a little warm water to it to warm it up enough to work in. Dice the celery.
Dice the cooked eggs to your size preference.
Add the mayonnaise, and yellow mustard to a medium bowl and whisk together until fully combined and creamy.
Add the salt, and black pepper to the mayonnaise mixture and whisk together to combine.
Add the diced eggs, diced celery, and half of the fresh parsley to the bowl with the dressing. Gently fold the ingredients together using a rubber spatula.
Wrap the bowl with plastic wrap or aluminum foil and refrigerate for at least 30 minutes before serving. *If time permits, let it sit overnight; it will improve the flavor. Garnish the egg salad with sweet paprika and finely chopped Italian parsley.
Serve on toasted bread, lettuce wraps, as an addition to a tossed salad, or as is.