Add the water, wine, olive oil, herbs, salt, and Parmesan in the bowl with the sponge. Mix thoroughly until well combined.
Gradually mix in one cup of flour, beating with a wooden spoon until the mixture is smooth.
Add the remaining flour, half a cup at a time, mixing well after each addition. The dough should be very soft.
Knead the dough for 5-6 minutes until it becomes smooth and elastic.
Leave the dough in the bowl, cover with a damp tea towel, and let it rise until doubled in size and full of bubbles, about 1 ½ to 2 hours.
Once risen, press the dough into a lightly oiled and parchment-lined 8-inch round or square cake pan or springform pan.
Cover the dough again with a damp cloth and let it rise until doubled, about 1 ½ to 2 hours.
Preheat the oven to 400°F (200°C) about 30 minutes before the dough is ready.
Using oiled fingers or knuckles, press deep dimples into the surface of the dough.
Drizzle a couple of tablespoons of olive oil over the dough, allowing it to pool in the dimples.
In a small bowl, toss the red onion slices and halved tomatoes with the remaining tablespoon of olive oil.
Arrange the red onion, tomatoes, and rosemary on top of the dough.
Sprinkle coarse sea salt over the top.
Bake the focaccia on the middle rack for 15 minutes at (200°C), then reduce the heat to 375°F (190°C) and bake for an additional 25 minutes or until golden brown.
Remove from the oven and let cool on a wire rack.