Place the water in the bowl of a stand mixer. Add the sugar, sprinkle the yeast over the water and let it bloom until bubbly, 5 to 15 minutes.
In a medium bowl, combine the 4 cups all-purpose flour and the wheat flour together with the salt and chopped rosemary. Gradually add the flour mixture to the bloomed yeast in the stand mixer. Then add 1/2 cup of the olive oil.
Using the dough hook attachment, mix the dough on medium speed until it becomes smooth and soft, 8 to 10 minutes. The dough will be very loose.
Transfer the dough to a clean, floured surface and knead by hand for 2 to 3 minutes.
Wipe out the stand mixer bowl and coat with some olive oil. Return the dough to the oiled bowl and let it rest in a warm place, covered with a dish towel, until doubled in size, 30 to 35 minutes.
Oil a 9-by-13-inch rimmed baking sheet with the remaining 1/2 cup olive oil. Spread the dough into the baking sheet using your fingertips to create dimples all over the dough. The more dimples you make, the more texture the bread will have.
Brush oil all over the dough with a pastry brush and sprinkle rosemary leaves into some of the dimples. Top with the tomato slices and sprinkle with the Parmesan. Cover the dough again with the towel and let rest in a warm spot until doubled in size, another 30 minutes.
Position a rack in the center of the oven and preheat to 425 degrees F.
Bake the dough until golden brown, 35 to 40 minutes.