1. Preheat oven to 500°F. Place a pizza stone or baking sheet in oven.
2. In a sauté pan, heat oil over medium heat. Add onion and sauté until translucent, about 12 minutes. Add vinegar, salt and pepper; stir and cook for 5 minutes. Remove from heat.
3. Roll out dough between 2 pieces of parchment paper to a 10-inch diameter. Remove top sheet of parchment and cover dough evenly with both cheeses, figs, walnuts, half the onions and oregano.
4. Reduce oven to 450°F and transfer pizza (on parchment) to pizza stone or baking sheet. Bake until cheese is golden and crust is crisp, about 12 minutes. Let rest for 5 minutes before slicing into 8 wedges and serving.