In a small bowl, combine the warm water, active dry yeast, and sugar. Stir gently and let it sit for 5 minutes until foamy.
In a large mixing bowl, whisk together the flour and salt.
Add the yeast mixture and 1 tablespoon olive oil to the flour. Stir with a wooden spoon until a shaggy dough forms.
Turn the dough onto a lightly floured surface and knead for about 7 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 grill to medium-high heat (about 400°F). Place a clean cast iron skillet on the grill to preheat for 5 minutes.
Lightly oil the cast iron skillet with olive oil to prevent sticking.
Roll out the dough on a floured surface to a size slightly smaller than your skillet (about 10 inches in diameter).
Carefully transfer the dough to the hot cast iron skillet on the grill.
Cook the dough on the grill with the skillet lid closed for 5 minutes until the bottom is golden and crisp.
Flip the dough using tongs or a spatula to cook the other side for 2 minutes.
Spread the pizza sauce evenly over the cooked side of the dough.
Sprinkle the shredded mozzarella cheese over the sauce.
Add the pepperoni slices, black olives, and green bell pepper evenly on top.
Sprinkle dried oregano over the toppings.
Close the grill lid and cook for an additional 8-10 minutes until the cheese is melted and bubbly and the crust is cooked through.
Remove the skillet from the grill carefully using heat-resistant gloves.
Let the pizza cool for 2 minutes before slicing and serving.