Place dough on a tray that's been lightly sprinkled with flour.  Cover with a dry cloth and place in a warm place until it comes to room temperature, about 2 hours.

Cut the dough into 18 rough pieces, weighing approximately 2.5 ounces each.  Set aside.

Tear the fresh mozzarella into small pieces.  Roughly chop the tomatoes and place them in a strainer that's been placed over a bowl.  Tear the ham into small pieces.

Form each piece of dough into a flat round disk.  Using a rolling pin, flatten each disk into a circle measuring about 4 1/2 inches in diameter.

Divide the torn mozzarella among the 18 circles of dough, placing it in a small mound in the center of each.  Divide the ham among 6 pieces of dough and place it on top of the mozzarella.  Divide the chopped tomatoes among the remaining 12 round of dough, topping off the mozzarella cheese.  Brush the edge of each circle with a small amount of water.  Fold in half and press down along the edge with a fork or a fluted edge pastry wheel to seal.

Heat oil in a large deep skillet or dutch oven to 375°.  Place 5 to 6 panzerotti in the heated oil and cook for 3 to 5 minutes.  Flip over and cook on the other side until golden brown, about an additional 2 to 3 minutes.

Remove from the hot oil with tongs and place on a paper towel-lined tray to catch any excess oil.  Serve immediately.  If not eaten right away, store fried panzerotti in an airtight container in the refrigerator for several days.  To reheat, place on a tray in a 350° oven for 8 to 10 minutes.