In a small bowl, combine warm water, sugar, and active dry yeast. Stir gently and let sit for 5 minutes until foamy.
In a large mixing bowl, combine flour and salt. Add the yeast mixture and 1 tablespoon olive oil. Stir until a dough forms.
Turn the dough onto a floured surface and knead for 5 minutes until smooth and elastic.
Place the dough in a lightly oiled bowl, cover with a clean towel, and let it rise in a warm place for 10 minutes.
Preheat your oven to 450°F (232°C).
Lightly oil a 10-inch cast iron skillet with olive oil.
Roll out the dough on a floured surface to roughly the size of your skillet.
Place the dough into the cast iron skillet, pressing it to cover the bottom and slightly up the sides.
Spread the pizza sauce evenly over the dough.
Sprinkle shredded mozzarella cheese over the sauce.
Add pepperoni slices, bell peppers, and black olives evenly over the cheese.
Place the skillet on the stovetop over medium heat and cook for 5 minutes to crisp the bottom of the crust.
Transfer the skillet to the preheated oven and bake for 12-15 minutes until the cheese is melted and bubbly and the crust is golden brown.
Remove the skillet from the oven carefully. Let the pizza cool for 3-5 minutes before slicing and serving.