Bake the Tater Tots as the label directs; let cool slightly.
Spread about 1/2 tsp. mustard on 1 slice of ham, then sprinkle with chopped dill pickle. Top with sliced cheese and cut lengthwise into 3/4 inch wide strips. Wrap each Tater Tot with one of the strips and secure with a toothpick.
Position a rack 6 inches from the broiler; preheat the broiler. Coat a baking sheet with cooking spray. Transfer the wrapped Tater Tots to the prepared baking sheet and broil until the ham starts crisping around the edges and the cheese melts, 2 to 3 minutes.
I found that the thinner the cheese is sliced, the easier these are to roll up.