Start by placing fresh large eggs in a medium saucepan and cover them with cold water, ensuring the water is about an inch above the eggs. Bring the water to a boil over medium heat, then cover the saucepan and remove it from the heat. Let the eggs sit covered for 12 minutes to achieve perfectly cooked yolks.

After the eggs have sat, carefully transfer them to an ice water bath using a slotted spoon. Let them cool for about 5 to 10 minutes.

Once the eggs are fully cooled, gently peel off the shells under running water if needed. After peeling, slice each egg in half lengthwise.

Scoop the cooked yolks out of each egg white into a mixing bowl. Use a fork to mash the yolks until completely smooth.

To the mashed yolks, add mayonnaise, softened cream cheese, Dijon mustard, olive brine, and vodka if using. Stir everything together until creamy and well combined.

With a spoon or piping bag, carefully fill each egg white half with the yolk mixture.

Sprinkle a dusting of paprika or smoked paprika over the filled eggs and add a juicy green olive on a cocktail pick atop each egg.

Place the garnished deviled eggs in an airtight container and refrigerate for at least 30 minutes before serving.