After the hour is up, and your dough has almost doubled in size, pull it from the oven and preheat the grill to 425°F.
Lay down a large piece of parchment paper on a flat surface and sprinkle with flour. Roll out the dough to the desired thickness. Roll up the edges to create a crust.
Drizzle on the olive oil and use a pastry brush or spoon to spread the oil on the crust. Evenly spread out the brie cheese. Spoon out a generous amount of jam (about half of the jar).
Slide the parchment paper with the pizza onto a baking sheet and transfer to the grill. Close the lid and grill for 5-10 minutes, checking to ensure the bottom is not burning.
Once cooked through, remove the pizza from the grill. Top with prosciutto and arugula, slice, and serve!