In a bowl, cream together the softened cream cheese and Italian dressing until smooth and well combined.
Fold in the chopped olives and pickle relish, mixing until evenly distributed throughout the cream cheese mixture.
Lay each ham slice flat and spread about 2 tablespoons of the cream cheese mixture evenly across the surface, leaving a small border at the edges.
Starting from one end, roll each ham slice tightly like you're making a jelly roll. The filling should spiral through the center. (Roll firmly but don't squeeze so hard that the filling oozes out the sides.)
Secure each roll with 4 toothpicks spaced evenly along the length. Wrap in plastic wrap and refrigerate for at least 3 hours to firm up.
Remove from refrigerator and use a sharp knife to slice each roll into 4 sections, keeping one toothpick in each piece. Arrange on a serving platter and serve chilled.
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