In a small bowl, combine the warm water, active dry yeast, and sugar. Stir gently and let sit for 5-10 minutes until foamy.
In a large mixing bowl, whisk together the flour and salt.
Add the yeast mixture and 1 tablespoon of olive oil to the flour mixture. Stir with a wooden spoon until a dough forms.
Turn the dough onto a lightly floured surface and knead for about 5 minutes until smooth and elastic.
Place the dough in a lightly oiled bowl, cover with a clean kitchen towel, and let it rise in a warm place for 15 minutes.
Preheat your grill to medium-high heat (about 400°F/200°C).
Lightly oil a 10-12 inch cast iron skillet with the remaining 1 tablespoon of olive oil.
Roll out the dough on a floured surface to fit the skillet size.
Place the dough into the cast iron skillet and spread evenly.
Spread the pizza sauce evenly over the dough.
Sprinkle the shredded mozzarella cheese over the sauce.
Top with pepperoni slices, black olives, and green bell pepper slices.
Sprinkle dried oregano evenly over the toppings.
Place the cast iron skillet on the grill grates and close the lid.
Grill for 12-15 minutes until the crust is golden and the cheese is melted and bubbly. Check occasionally to avoid burning.
Remove the skillet from the grill using oven mitts and let the pizza cool for 2-3 minutes.
Slice and serve hot.