Divide your dough into two equal portions and roll into a ball, set on a lightly-floured surface and cover with a towel. Bring to room temperature for about 1 hour prior to cooking.
Heat griddle or grill to medium-high heat (or heat the oven to 500 degrees and put the rack on the lowest rung). If you’re using the oven here, you’ll want to start pre-heating it at least 30 minutes early.
Shape your dough into 2 round, rectangle, or oblong shapes. Prick bottom with a fork to prevent giant bubbles from forming when you cook the dough.
Grill your bread until poofed and browned on one side, then flip and cook the other side. If you’re using the oven, it’s pretty much the same concept, you can leave it in there un-flipped just keep cooking until both sides are lightly-browned and the dough is cooked through. You’ll have to do this twice, because there are two pieces of dough. If you’re using the grill it only takes a few minutes per side, super easy! Let it cool slightly, until you can handle it comfortably. (You can also make the flatbread one day ahead and top it the next day).
Using a knife or the back of a spoon, spread a layer of mascarpone on the flatbread. Then spread a layer of fig jam over the layer of mascarpone. They’re going to mix together, it’ll be okay. You’re halfway there.
Now you have two options, prosciutto and then arugula, or arugula and then prosciutto. I prefer the latter as I find that putting the prosciutto on top helps to hold the arugula onto the flatbread. If I put the arugula on top I end up chasing it around as it falls off of every bite I take.
Then, that’s it! You’re done! Slice it up and eat it.