Combine the water, yeast, and honey in a large bowl. Stir in just enough of the bread flour to make a batter about the consistency of buttermilk. Cover and let proof in a warm place until the surface is puffy, about 1 hour.
Add the remaining bread flour, the semolina flour, and the salt. Knead in a stand mixer fitted with dough hook on medium speed, or by hand, until the dough is smooth, springy, and elastic, 4 minutes with the mixer or 10 minutes by hand. Rub the dough lightly with oil, place in a clean bowl, and cover with a cloth.
Let the dough rise at warm room temperature until doubled in volume, about 1 1/2 hours.
Punch down the dough, sinking your fist into it to deflate it, and divide into 4 equal pieces for individual pizzas or leave it whole for a large pizza. Form the dough into smooth ball(s), cover, and let rise again until doubled in volume, 45-60 minutes.
Preheat the oven to 450°F. Lightly oil a 16-inch pizza pan or large baking sheet with vegetable oil or scatter with cornmeal.
On a lightly floured surface, roll and stretch out the ball(s) of dough to an even 1/4-inch thickness. If the dough has not relaxed properly, it may spring back as you stretch it; simultaneously spinning and stretching the dough will help. (This may be accomplished flat on a work surface or by spinning and tossing it into the air, then catching the disk on the back of your hands. Avoid tearing the dough or creating very thin patches.)
Transfer the dough round to the prepared pan.
For the topping, mix together the olive oil, basil, oregano, garlic, and pepper to taste.
Spread this mixture evenly over the pizza dough.
Spread evenly with the tomato purée and top with the sliced tomatoes and mozzarella. Scatter the Parmesan over the top.
Bake until the dough is golden brown and the toppings are very hot, 20-30 minutes for 1 large pizza or 10-12 minutes for individual rounds.
Cut into wedges and serve at once, or let cool for 5-10 minutes and serve warm.
