Using a round pastry cutter, cut the pastry into 2-inch rounds. Roll the remaining scrap into a ball and roll out with a rolling pin into a 1/4-inch thick sheet and continue to cut rounds of puff pastry until you've used up all of the pastry. As you cut the pastry, place it on a cookie sheet lined with waxed paper and refrigerate it until the filling has been made.
For the filling, put the remaining ingredients, except the egg wash, into a food processor and pulse for 1 to 2 minutes to combine well. Scrape the sides of the bowl carefull with a rubber spatula and pulse again briefly.
Heat a deep fat fryer to 365 degrees.
Lightly brush a round of pastry with some of the egg wash. Place 1 teaspoon of the ham filling in the center of the round and fold the dough in half to create a dumpling. Continue to fill the pastry in this way until all of the filling and pastry has been used up. Place the finished turnovers on a parchment paper-lined cookie sheet, brush the tops with the remaining egg wash, and deep fry in batches for several minutes until rich golden brown. Drain on paper towels and serve immediately.
Recipe courtesy of Michael Lomonaco