In the bowl of a food processor, combine pastrami, sauerkraut, pickles, salt, and pepper. Pulse for 10 seconds, until roughly chopped. Transfer mixture to a small bowl.

Place egg roll wrappers on a work surface. Place a heaping tablespoon of filling in the center of each wrapper. Using a pastry brush, brush the edges with beaten egg. Fold egg- roll-style (look on package for a diagram and instructions). Alternatively, you can use wonton wrappers and make small wrappers or dumplings.

Heat oil in a deep fryer or pot one-fourth of the way full. When oil is very hot, add pastrami wrappers and fry until golden on each side. Drain on a paper towel-lined plate.

In a medium bowl, combine all ingredients and whisk together very well. Serve alongside pastrami wrappers.