Preheat oven to 400˚F (200˚C). Grease a 9x13 inch (23x33 cm) rimmed baking sheet with olive oil or line with parchment.
Press the risen dough into the prepared pan in a thin, even layer. Gently continue to stretch it out to fit all sides without tearing. Use your fingers to press down into the dough all over to create dimples across the surface of the dough.
Lightly cover the pan with a towel and allow to rest at room temperature until puffed, about 30 minutes.
In a large bowl, toss together the tomatoes, onions, oregano, salt, pepper, and olive oil until well coated.
Evenly spread the tomato and onion mixture across the surface of the prepared dough, keeping the edges clear. Bake in preheated oven until golden, about 40 minutes. Remove from heat and lightly drizzle the top of the bread with additional olive oil.
Allow the bread to sit at room temperature for 5 minutes before slicing and serving.