In a large mixing bowl, combine the warm water and active dry yeast. Let sit for about 5 minutes until frothy.
Add the flour, salt, and olive oil to the yeast mixture. Stir until a dough forms.
Knead the dough on a floured surface for about 5 minutes until it becomes smooth and elastic.
Place the dough in a lightly greased bowl, cover it with a damp cloth, and let it rise for about 15 minutes.
Preheat the grill to medium-high heat (about 400°F / 200°C). If using a pizza stone, place it on the grill to heat up.
Roll out the dough into a 12-inch round on a floured surface. If necessary, use parchment paper to transfer the dough to the grill easily.
Carefully place the rolled-out dough onto the grill and cook for 3-4 minutes until the bottom is golden and grill marks appear.
Flip the dough using tongs, and immediately spread pizza sauce over the grilled side. Sprinkle with mozzarella cheese and add your desired toppings.
Close the grill lid and cook for an additional 3-5 minutes until the cheese is melted and bubbly.
Carefully remove the pizza from the grill. Garnish with fresh basil leaves, slice, and serve hot.