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In a stand mixer, whisk together the flours, salt, sugar, Italian seasoning, and yeast. Change the attachment to the dough hook. Measure the water and oil together and then with the motor running on medium speed, gradually add the water mixture and continue to mix until a soft dough forms.
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If the dough appears a bit dry and shaggy, add about 1 Tbsp of water at a time until the dough comes together. If it's too wet and sticky, you can add a little more flour until you have a soft, smooth, dough. Run the mixer for about 3-4 minutes to knead it well. If you are making the dough by hand, knead it for about 5-7 minutes.
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Take the dough out of the mixing bowl and shape into a large ball. Coat a large bowl with olive oil and then set the dough inside, turning in and rubbing against the bowl to coat it in oil as well. Cover with cling film and set the bowl in a cold oven with the light turned on. The heat from the light will be enough to give the dough a warm environment to rise.
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Let the dough rise for 70-90 minutes, or until doubled in size.
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While the dough is rising, prep the veggies and grate the cheese. Arrange the vegetables on a large platter. Keep the cheese in the fridge so that it's chilled.
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When the dough has risen, take the bowl out of the oven and turn the oven to 450 F. Divide the dough into two pieces and on a lightly floured counter knead them a bit to get out the extra air.
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Using a rolling pin, roll out and stretch the dough to fit two 12 inch pizza pans. Stretch the dough to the edge of the pans, creating a rim by pressing around the edges with your fingers.
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Lightly spread about 2-3 tsp olive oil over the pizza crust. Next,spread about 1/3 cup sauce on each pizza, covering each to the edges. Top the pizza with the mozzarella. Next top with the peppers, garlic, onions, tomatoes, and other vegetables. Lastly, sprinkle the Parmesan cheese over each pizza.
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Bake the pizzas in the lower 1/3 and middle of the hot oven for 8 minutes before switching the pans and baking another 8 minutes. Check the crusts to see that they are golden brown.
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Take the pizzas out of the oven and turn the oven on to broil. Move the top rack up so that it's about 6 inches away from the broiler. Watch it very, very carefully.
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When the cheese has caramelized a little, remove from the oven and let cool for about 3-5 minutes before slicing into pieces