Stir together the sour cream, chives, mustard, horseradish and a few grinds of black pepper in a small bowl.
Lay four slices of jicama out on a work surface. Spread each with some of the mustard-horseradish sauce, top each with 1/4 of the ham, a slice of cheese, and about 1/2 cup of arugula. Sandwich with the remaining jicama slices, cut in half and serve with a pickle spear if using.
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