Preheat your grill to HIGH.
On a lightly floured cutting board OR a cookie sheet, shape the pizza dough by flattening it with your hands.
When the grill is HOT, brush the grates with olive oil.
Slide the pizza dough off the cookie sheet (or off the cutting board) and onto the hot grill grates. Close the lid and cook for 2 minutes.
Open the grill and see if the bottom of the pizza dough is lightly browned; if not, give it another minute to cook.
Remove pizza dough from the grill and transfer it back to the cookie sheet; flip it over so that the grilled side is now facing you. Keep your grill covered to retain heat.
Brush pizza dough with olive oil. Spread pizza sauce over the dough.
Add a layer of shredded cheese over the sauce. Arrange prepared ham, mushrooms, olives and artichokes on top of the cheese.
Slide the pizza back onto the grill.
Turn heat down to medium-high, and close the lid.
Cook for 3 to 4 minutes, or until cheese is melted.
Remove pizza from the grill and onto a cutting board. Garnish with a sprinkle of dried oregano, if desired.
Let rest for 2 minutes before cutting.