In the bowl of a stand mixer, whisk together the flours, semolina, yeast, sugar and salt.
Add the warm water and stir, just until it starts to come together.
Fit the dough hook to the stand mixer and mix on low speed for about 5 minutes until the dough comes together in a smooth ball. The dough should still be a little sticky and will stick to the bottom of the bowl, but if will not come away from the sides at all, add more flour, one tablespoon at a time, mixing until it comes together. Do not add too much flour or the crust will be tough.
Drizzle a little olive oil down the inside of the bowl and roll the ball of dough around to coat the dough and the inside of the bowl.
Cover the bowl with a tea towel and put in a warm place to rise for 45 minutes to an hour, until doubled in size.*
Towards the end of the rising time, place a pizza stone on the middle rack of the oven, and preheat the oven and pizza stone to the highest temperature it will go (mine goes to 550F).
Once it has doubled, punch the dough down and form it back into a ball. Sprinkle a little semolina onto a large piece of parchment paper. Using your fingers, form the dough into a 12-inch circle on top of the parchment.
Let the dough rest for 10-15 minutes before adding the toppings. This will allow your dough to rise a little more and ensure a soft, thick crust.
Spread pizza sauce over the dough. Add a layer of toppings if using. Sprinkle the mozzarella over the toppings. Add a second layer of toppings if desired, and sprinkle with the Parmesan cheese.
Using the parchment paper to lift, transfer the pizza and parchment paper to a pizza peel, wooden cutting board, or the back of a large baking sheet. Open the oven door and carefully slide the pizza and parchment onto the hot baking stone.
Bake 8-12 minutes until golden and cooked through. Time will depend on how hot your oven is, and on whether you are baking on a preheated stone or using a pizza pan. At 550F, mine takes 8 minutes.