Slice the onions and place them in a large sauté pan over medium low heat with the butter. Cook the onions slowly, stirring occasionally, for 35-40 minutes until they are a deep caramel brown. This slow process brings out their natural sweetness. I recommend not rushing this step—the longer you cook the onions, the better the flavor.
Add the packed brown sugar and balsamic vinegar to the caramelized onions from Step 1. Continue cooking for 3-5 minutes, stirring, until the onions become sticky and thick. Remove the mixture from the pan and set aside to cool.
Preheat your oven to 425°F. Drizzle a sheet pan with olive oil. Open the tube of thin crust pizza dough and roll it out onto the pan. Drizzle with additional olive oil and press the dough out to the edges. Sprinkle evenly with garlic powder.
Sprinkle 1 ½ cups of shredded mozzarella or fontina cheese over the stretched dough. Spread the prepared caramelized onions from Step 2 evenly on top. Arrange the fresh fig slices across the pizza, then add the remaining shredded cheese and 6 oz of the goat cheese (crumble it as you go). Tear the prosciutto and basil leaves and scatter them evenly over the pizza. Drizzle with olive oil for extra richness.
Place the assembled pizza in the preheated oven and bake for 15-17 minutes, or until the crust is golden brown and the cheese is bubbling. For an extra crispy crust, I like to bake it on the lowest oven rack for the last few minutes.
Once the pizza is out of the oven, top it with arugula, the reserved goat cheese, a drizzle of olive oil, and finish with balsamic glaze. Slice and serve immediately for the freshest flavor.