2½ cups water
1½ cups rice vinegar
1 teaspoon yellow mustard seeds
1 teaspoon whole black peppercorns
1 teaspoon whole allspice berries
2 dried bay leaves
½ cup granulated sugar
¼ cup kosher salt
6 large eggs
½ cup mayonnaise
½ teaspoon Dijon mustard
¼ teaspoon cayenne pepper
1 teaspoon kosher salt
3 slices white sandwich bread, lightly toasted and cut into quarters
Sweet paprika, for serving
1. Make the pickled eggs: In a medium saucepan set over medium heat, add the water, rice vinegar, mustard seeds, black peppercorns, allspice berries, bay leaves, sugar and salt. Bring to a simmer, stirring often, until the sugar and salt dissolve. Turn off the heat and pour the pickling liquid into a medium heat-safe bowl. Refrigerate until completely cooled.
2. Fill a large bowl with ice and water and set aside. Bring a medium saucepan of water to a boil over high heat. Reduce the heat to medium-high and use a slotted spoon to slowly lower the eggs, one at a time, into the water. Simmer for 10 minutes, turn off the heat, and use a slotted spoon to transfer the cooked eggs to the large bowl of ice water to chill. Once the eggs are cool enough to handle, roll them on a counter to crack the shell, then peel it away. Add the peeled eggs to the cooled pickling liquid, cover the bowl with plastic wrap and refrigerate for 24 hours (or up to several days).
3. Make the egg salad: Remove the eggs from the pickling liquid (discard the liquid) and place them on a paper towel to dry. Set a box grater in a large bowl and grate the eggs on the side with the medium-size holes. To the grated eggs, add the mayonnaise, mustard, cayenne and salt, and stir to combine. Slather onto the toasted bread and serve sprinkled with a pinch of paprika.