To make the dough, pour the warm water into the bowl of a stand mixer. Sprinkle the yeast over the water. Let sit for 5 minutes.
Add the flour, then the salt.
With the mixer fitted with the hook attachment, mix on medium-low (2nd gear on the KitchenAid) until a ball is formed, about 1 minutes. Once all ingredients are incorporated and a ball is formed, mix 8 minutes.
Transfer to an oiled bowl. Cover with plastic wrap. Let rise until doubled in size.
Turn out onto a floured surface and divide into 4 equal portions. Roll each half into a ball, place in an oiled container. Cover. Refrigerate at least 30 minutes before use.
Remove the metal grease shield from the Kamado Joe Pellet Joe. Fire up the grill, set to 450°F. When the grill comes up to temp, allow to preheat for 20 minutes to get the dome hot. Install the Kamado Joe DoJoe attachment after the 20 minute preheat. Make sure the deflector plates are in place underneath the pizza stone. Give the grill another 20 minutes to preheat the stone. You can use an infrared thermometer to read the temperature on the surface of the stone. Aim for 450°F.
To make the sauce, combine all ingredients in the Vitamix and blend until smooth. Transfer to a small skillet. Bring to a simmer. Cook to desired consistency, about 5-10 minutes.
On a floured work surface, stretch your pizza dough thin to about 12” across. Transfer to a floured pizza peel. Spread your pizza sauce over the dough. Top with mozzarella and pepperoni. Brush the edge of the crust with Sicilian Extra Virgin Olive Oil. Sprinkle parmesan over the oil. Make sure the peel is free of oil or sauce, as this will cause it to stick to the peel. Transfer the pizza to the grill.
Cook the pizza for about 5 minute. Spin the pizza halfway around. Cook until the bottom is browned and cheese is melted and browning on top, about 10 minutes total.
Repeat the process with the remaining pizzas. The pizza stone temperature will recover in the time it takes to build the next pizza.