Directions

• For brine, drain beet juice into a small saucepan; set beet slices aside. Add the ½ cup vinegar, sugar, salt, and peppercorns, and bring to a low boil over medium heat, stirring until sugar dissolves, 3 to 5 minutes. Let cool completely, about 20 minutes.
• Place eggs in a jar or glass bowl just large enough that brine will completely cover eggs; pour in brine. Top up with vinegar as needed to cover eggs completely. Refrigerate, covered, for at least 12 and up to 24 hours. The longer eggs are in brine, the deeper pink they will be.
• Slice eggs in half lengthwise from top to bottom with a sharp knife. Remove yolks and place in a bowl. Mash yolks with a fork until smooth, and stir in mayonnaise, Dijon, the 1 teaspoon vinegar, and hot sauce; season with salt and pepper. As an option, if you have a small food processor, place all filling ingredients in it, and blend until smooth.
• Spoon filling evenly into egg whites or add mixture to a piping bag or resealable plastic bag with one corner clipped. Pipe mixture into egg white halves, garnish as desired, and serve.