Build a fire in the wood oven and build the temperature up to about 700°F.
In a small saucepan, reduce the balsamic vinegar over medium-low heat by about two-thirds, until syrupy. Set aside.
Place the dough disk on a lightly floured surface and press out into a rough oval shape, a little less than ¼ inch thick (if the dough resists your efforts to press it out thin, cover with a towel and leave to rest for about 5 minutes, then persist).
Dimple with your fingers every inch or so, leaving the edge untouched, and brush all over with olive oil.
Transfer the dough round to a wooden pizza peel liberally scattered with cornmeal.
Don’t press down on the dough at all as you load and top it, or it will stick to the peel.
Immediately scatter the dough with the sliced figs, prosciutto, and mozzarella.
Quickly and confidently slide the pizza onto the floor in the center of the oven and bake for about 5 minutes, rotating occasionally after the first minute or two.
As soon as the edges of the first pizza are nicely charred and the cheese has melted, remove from the oven.
Scatter with the arugula and drizzle with a little balsamic syrup.
Cut and serve.
Alternate Method: Bake the pizza at the hottest setting your oven will achieve, preferably set to convection. It will take longer than 2 to 4 minutes, probably 6 to 8. Best results will be obtained with a fully preheated baking steel, set on the oven’s lowest shelf.