Lightly grease a 9" x 13" pan, and drizzle 1 to 2 tablespoons olive oil in the bottom. (I like to line the pan with foil that comes over the edges so I can lift the bread out and cut it with a pizza cutter.)
Combine water, olive oil, salt, flour, yeast, 2 TBS Parmesan cheese, onion and garlic powder, and Italian seasoning. Mix on high speed with an electric mixer for 60 seconds.
Scoop the sticky batter into the prepared pan, cover the pan, and let it rise at room temperature for 60 minutes, till it's become puffy.
While the dough is rising, saute sliced onions in 1-2 TBS of olive oil over medium-high heat until they begin to turn golden, lower heat. Then add balsamic vinegar and cook until the liquid has evaporated.
Preheat the oven to 375°F
Gently poke the dough all over with your finger tips.
Drizzle it lightly with olive oil, and top with onions and some fresh ground pepper and little bit of salt. Sprinkle on some Parmesan cheese, if desired.
Bake the bread till it's golden brown, 35 to 40 minutes.
Remove it from the oven, wait 5 minutes, then cut into squares. Serve warm or at room temperature.