An hour before you want to make the pizza, take the dough out of the fridge. On a clean surface, shape it into a ball and place it on a sheet pan dusted with all-purpose flour. Dust the top with more flour and cover with a clean kitchen towel (not terrycloth). Place somewhere warm to rise.
When ready to make the pizza, preheat your grill on high heat, about 550°F. Clean the grill grates.
On a lightly floured surface, press and stretch the dough out to a round about 10 inches in diameter. If the dough tears just pinch it back together.
Flip a large sheet tray upside down so the rimmed edge is facing down and liberally sprinkle with semolina and all-purpose flour (you can also use a pizza peel or large cutting board for this). Carefully place the dough onto the sheet tray and press back into a circle if needed. Make sure the pizza can easily slide around on the pan.
Quickly slide the dough onto the grill grate, close the lid and cook until the bottom is charred and the top is puffed, 3 to 4 minutes. Using a large spatula, transfer the pizza to the sheet pan and flip, so the grilled side is now facing up. Spread with the sauce, making sure to spread to the edges. Top with the cheese, a sprinkle of salt and pepper, and finish with a drizzle of olive oil.
Lower the heat on the grill to about 500°F. Place the pizza back on the grate. Close the lid and cook until the cheese is melted and bubbling and the bottom of the pizza is golden brown and crispy, 4 to 5 minutes.
Remove and sprinkle with freshly grated Parmesan cheese, a little more salt, and freshly cracked black pepper. Finish with the basil leaves and cut into 6 wedges.