In a small bowl, combine warm water, active dry yeast, and sugar. Stir gently and let sit for 5-10 minutes until foamy.
In a large mixing bowl, combine flour and salt. Make a well in the center and add the yeast mixture and 1 tablespoon olive oil.
Mix together until a dough forms. Transfer to a floured surface and knead for 8-10 minutes until smooth and elastic.
Place dough in a lightly oiled bowl, cover with a clean kitchen towel, and let rise in a warm place for 1 hour or until doubled in size.
Preheat your oven to 475°F (245°C). Place your cast iron pizza pan in the oven to heat for 10 minutes.
Punch down the risen dough and transfer it to a lightly floured surface. Roll or stretch the dough into a circle slightly smaller than your cast iron pan (about 10-12 inches in diameter).
Remove the hot cast iron pan from the oven carefully. Add 1 tablespoon olive oil to the pan and swirl to coat the bottom and sides.
Place the dough into the pan, pressing it to fit and slightly up the sides.
Spread the tomato sauce evenly over the dough, leaving about 1/2 inch border around the edges.
Sprinkle the shredded mozzarella cheese evenly over the sauce.
Distribute the sliced mushrooms, green bell pepper, and black olives over the cheese.
Sprinkle dried oregano, garlic powder, and crushed red pepper flakes evenly on top.
Place the cast iron pan back into the oven and bake for 15-20 minutes until the crust is golden and cheese is bubbly and slightly browned.
Remove the pan from the oven and let the pizza cool for 5 minutes before slicing and serving.