Preheat grill to 425 degrees F.
On a lightly floured surface, roll the dough balls into 6-inch circles. Place rolled dough on a floured pizza peel or the back of a baking tray.
Using a small spatula, spread the duxelle on the dough circles evenly, leaving about a half inch around the edges uncovered. Sprinkle on the cheese (leaving a small amount for later) and place your garnishing mushrooms on top.
Lightly oil a pizza stone with extra virgin olive oil and place the pizzas on the stone. (You can grill directly on the grill racks if desired. If doing so, clean the racks thoroughly with a wire brush.)
Cook for 5 minutes. You might need to cook the pizzas in batches depending on the size of your grill
Open the grill and sprinkle the remainder of the cheese over the pieces, then close the grill and cook for 2-3 minutes, or until the sides of the pizza are golden brown and all the cheese is melted. Remove from the grill and lightly brush the crust with the garlic oil. Garnish with arugula leaves and enjoy.