Prepare pizza dough; begin proofing yeast by dissolving yeast and sugar in warm water. When puffed up and foamy, add olive oil to proofed yeast.
In the bowl of a stand mixer, combine dry dough ingredients. With mixer running on low, slowly add liquid ingredients. Mix until a smooth ball forms and pulls away from the sides of the bowl. Add additional flour as needed. Transfer dough to a lightly greased bowl. Cover and allow to rise in a warm location until doubled or roughly 1 hour.
Begin preparing filling while dough rises. In a medium skillet over medium heat, brown mushrooms with olive oil and salt to taste. Remove to a large bowl. Using the same skillet, saute sausage in 1 Tbsp olive oil. Drain and transfer to the bowl with mushrooms. Saute onion, pepper and garlic with optional red pepper flakes for 10 minutes or until tender. Transfer to large bowl, mix with sausage, mushrooms, 1 cup mozzarella, basil, oregano and 1/2 cup crushed tomatoes. Cover and set aside.
When dough has doubled in size, preheat oven to 450 degrees. Lightly grease a 9" springform pan. Shape dough to fit the bottom of the pan and at least 3/4 up the sides. Lightly fork dough throughout. Bake for 10 minutes at 450°F.
Reduce heat to 400°F. Lin the crust with ham. Top off with sausage mixture. Cover with additional 1/4 cup crushed tomatoes. Sprinkle with remaining mozzarella and Parmesan cheese. Bake for 35-40 minutes or until cheese is fully melted and crust is golden and crisp.
Allow to cool for 10 minutes prior to removing the sides of the pan and slicing. Slicing on a cutting board with drain grooves is recommend for this pizza.