Place a pizza stone on the grill and preheat your grill to medium-high heat (around 400°F). See note if not using a pizza stone!
Place the dough ball on the floured pizza peel or floured sheet of parchment paper (this makes it easier to transfer for grilling). Gently press it down into a flat disc, about 6 inches wide. Use a rolling pin to roll it out into a circle about 12–14 inches in diameter, rotating the dough a quarter turn after every few rolls to keep it round. Try not to roll it too thin or you'll lose the chewy texture.
Spread the marinara evenly over the dough, leaving a small border around the edges. Layer on the mozzarella and provolone cheese, followed by a generous spoonful of the olive mix. Add the sopressata and salami slices on top. Brush the outer crust edges with olive oil and sprinkle with sesame seeds so they adhere.
Transfer the pizza directly to the baking sheet or the preheated pizza stone and cook with the lid closed for about 10 minutes, or until the crust is golden and crisp and the cheese is melted and bubbly.
Remove the pizza from the grill and finish with extra olive mix and mounds of sliced mortadella. Slice and serve warm.