Pizza dough:

1. In a large bowl of a stand mixer fitted with the flat beater attachment, combine the flour, water, yeast, sugar and salt.  Mix until sticky dough forms without any dry flour, less than 1 minute.  
2. Add dough hook to stand mixer and knead dough for 3-4 minutes on low speed.  Add a small amount of flour if dough is too sticky.
3. Place dough in medium bowl and cover top with plastic wrap.   Let the dough rise at least 30 minutes or until double in size.
4. Turn the dough out onto a lightly floured work surface.  Gently press down dough.
5. Shape dough into a ball by folding the edges into the center.  Turn the dough seam-side down and cover and let rest for at least 20 minutes and up to 1 hour, until relaxed enough to stretch.

Grilled Heirloom Tomatoes:

While pizza dough is rising, roast the heirloom tomatoes.

1. Preheat grill to medium-high and oil grates with tongs and folded paper towel coated in cooking oil.  
2. Drizzle olive oil mixture over tomato slices.  
3. Cook tomatoes on pre-heated grill until they start to sizzle, about 3 minutes.  Flip tomatoes over and grill for another 2 minutes.   Set aside.

Grilled Pizza:

1. Preheat gas grill to 350°F and adjust one burner to medium-low and other to medium-high.
2. In a small bowl whisk together the olive oil and garlic and set aside.
3. Place parchment paper on pizza peel or wooden cutting board.  Transfer dough to peel and shape into a 12-inch circle.
4. To grill the pizza, lightly brush the shaped dough with the basting oil and transfer pizza with parchment paper underneath to the less-hot section of the grill and bake for 4-5 minutes until the bottom crust is golden brown.  Trim parchment paper before placing on grill grates.   Keep the grill lid closed while grilling.
5. Remove pizza from the grill with a pizza peel and gently flip over with tongs until cooked side is facing up.  
6. Add toppings:   Arrange roasted tomatoes and add mozzarella slices and fresh basil.  Sprinkle on parmesan cheese.
7. Place the pizza back on the grill and cook with lid closed for an additional 4-5 minutes or until the crust is golden in color and cheese is melted.  Move pizza to hotter section of grill for desired crispiness and color.
8. Remove pizza from grill and brush outer crust with basting oil if desired.