In a large skillet, drizzle the 2 tablespoons (30 milliliters) olive oil over medium heat.
Add the thinly sliced onions to the pan. Cook, stirring occasionally, until softened but not brown.
Stir in the oregano, salt, and pepper. Remove from heat and set aside to cool slightly.
Preheat oven to 450˚F (230˚C). Grease a 14 inch (35.5 centimeter) round baking sheet or pizza pan with olive oil.
Divide the risen dough into 2 separate pieces, one slightly larger than the other. Cover the smaller piece of dough and place the larger piece on a lightly floured work surface.
Stretch the larger dough into a thin circle, about 12 inches (30.5 centimeters) wide, and place in the prepared pan.
Evenly cover with 3/4ths of the shredded mozzarella cheese, leaving a 1/2-1 inch (1.25-2.5 centimeter) border around the edges.
Stretch the smaller piece of dough into a circle large enough to cover the layer of cheese.
Fold the edges of the bottom circle over the top circle and pinch together to seal in the cheese.
Prick the top all over with a fork. Bake in the preheated oven for 5 minutes.
Remove the pizza from the oven and evenly top with the onions, Sprinkle with the remaining 1/4 mozzarella cheese. Lightly drizzle with olive oil.
Place back in preheated oven and bake until the crust is golden and the top layer of cheese is bubbly and browned, about 10-15 more minutes.
Serve the Fugazzeta warm from the oven.