In a large mixing bowl, combine the warm water and active dry yeast. Stir gently and let it sit for 5 minutes until foamy.
Add the bread flour, sugar, salt, and 2 tablespoons of olive oil to the yeast mixture. Mix until a sticky dough forms.
Turn the dough onto a lightly floured surface and knead for about 8 minutes until smooth and elastic. Alternatively, use a stand mixer with a dough hook for 5 minutes.
Place the dough in a lightly oiled bowl, cover with plastic wrap or a damp towel, and let it rise in a warm place for 1 to 1.5 hours, or until doubled in size.
Preheat your oven to 500°F (260°C). Place a 10-inch cast iron skillet in the oven to heat for 10 minutes.
Once the dough has risen, turn it out onto a lightly floured surface and gently stretch it to fit the size of your cast iron skillet (about 10 inches).
Carefully remove the hot skillet from the oven and grease it generously with olive oil.
Place the stretched dough into the skillet, pressing it to the edges. The dough will be thick and airy.
Evenly distribute the shredded mozzarella and grated brick or Monterey Jack cheese over the dough, making sure to cover the edges to create a crispy cheese crust.
Bake the pizza in the oven for 15 minutes.
Remove the pizza from the oven and spoon the tomato sauce evenly over the cheese in three stripes or dollops.
Sprinkle dried oregano, garlic powder, and crushed red pepper flakes (if using) over the sauce.
Return the pizza to the oven and bake for an additional 10 minutes until the cheese is bubbly and golden brown.
Remove the pizza from the oven and let it cool for 5 minutes before slicing and serving.