2. Add the flour, salt and olive oil. Mix together with the wooden spoon until the dough is too thick and sticky to stir.
3. Spread a little flour on a work surface and place the dough on top of the flour. Knead the dough by pulling it from the sides and folding it in the middle. Keep kneading until the dough becomes a smooth ball. If it sticks to the table or to your hands, add a little more flour.
4. Rub a clean bowl with the olive oil and put the dough in it. Cover the bowl with a towel and put it in a warm place. Let the dough rise for about 1 1/2 hours, or until doubled in volume.
5. Punch the raised dough down with your fist. Turn the dough over, form it into a ball again, cover, and let rise for another hour.
6. Spray the grill grate with nonstick spray and preheat the grill to medium.
7. Roll out the dough with a rolling pin or use your hands to pat the dough into a circle about 12" to 14" across and 1/4"-thick.
8. Lightly drizzle one side of the dough with olive oil and carefully place the dough, oil side down, on the grill. Lightly drizzle the other side of the dough with olive oil (the side facing up).
9. When the dough is golden brown on one side, turn it over using a long spatula.
10. Arrange the tomato slices and mozzarella cheese on top of the pizza, sprinkle with salt, pepper and olive oil, place the cover on the grill and cook until the crust is golden brown and the cheese is melted, about 5 minutes.
11. Using a long spatula or 2 smaller ones, remove the pizza from the grill and sprinkle the basil leaves over the top. Cut into slices and serve.