Preheat the grill to medium-high heat.
Brush the inside of a 12-inch cast iron skillet with 1 tablespoon of avocado oil.
On a lightly floured surface, roll out the pizza dough to fit the size of the skillet.
Carefully transfer the rolled-out dough to the prepared skillet, pressing it into the bottom and up the sides of the skillet.
Spread the pizza sauce evenly over the dough, leaving a small border around the edges.
Sprinkle 1 cup of the shredded mozzarella cheese over the sauce.
Evenly distribute the sliced pepperoni over the cheese.
Drizzle the remaining 1 tablespoon of avocado oil over the toppings.
Carefully place the skillet on the grill and close the lid.
Grill for about 12-15 minutes, or until the crust is golden and the cheese is melted and bubbly. Rotate the skillet occasionally for even cooking.
Once the pizza is cooked, carefully remove the skillet from the grill using oven mitts or heat-resistant gloves.
Allow the pizza to cool for a few minutes before garnishing with fresh basil leaves.
Optionally, serve with grated Parmesan cheese sprinkled on top.