Set the pot over medium-high heat and bring to a boil. Gently stir the eggs occasionally during this process to help center the yolks.

Once the water reaches a rolling boil, cover the pot with a lid, turn off the heat, and let the eggs sit in the hot water for 14 minutes.

While the eggs are sitting, fill a large bowl with ice and cold water to create an ice bath.

After 14 minutes, use a slotted spoon to transfer the eggs to the ice bath. Let them cool for at least 5 minutes to stop the cooking and make peeling easier.

Peel the eggs under running water, then gently pat them dry with a paper towel.

Using a sharp knife, cut each egg in half lengthwise. Carefully remove the yolks with a small spoon and place them in a medium bowl. Set the egg white halves on a serving platter.

Add the mayonnaise, mustard, distilled white vinegar, and kosher salt to the bowl with the yolks. Mash everything together with a fork until smooth, then whisk until fully combined. For an extra smooth texture, you can use a handheld mixer.

Spoon or pipe the yolk mixture evenly into the wells of the egg whites using a small spoon or a piping bag fitted with a large round tip.

Sprinkle paprika and chopped fresh chives over the filled eggs, if using. Serve immediately, or refrigerate in an airtight container until ready to serve.