To make the dough, combine the flour, sugar, and yeast in the bowl of a food processor fitted with the metal blade. Pulse to combine.
With the machine running, add the ice water through the feed tube and process until the dough is combined everything is incorporated, about 10 seconds. Let dough rest for 10 minutes.
Add the salt and vegetable oil and process until the dough forms a smooth, tacky ball that doesn't stick to the sides of the bowl anymore. Remove the dough from the bowl and knead for 1 minute on a lightly oiled or floured work surface then transfer it to a lightly oiled bowl, cover, and refrigerate for 24 hours or up to 3 days. (AFTER the refrigeration process, the dough can be wrapped tightly in plastic wrap, put in a freezer bag, and frozen for later use.)
To make grilled pizza with this dough, preheat your outdoor grill to high heat. Roll out your dough on a lightly floured & cornmeal sprinkled 9-inch pizza pan. Gently stretch it and pull it to fit the 9-inch pizza pan.
Once done, place it gently on the grill (you may need a helping hand for this part). Close the lid and grill for 3-5 minutes on each side (checking every so often to make sure the bottom doesn't get too charred - every grill VARIES in temperature so keep an eye on it).
After 3-5 minutes, flip the dough on the other side, close the lid and grill for another 3-5 minutes, again checking every so often to make sure it doesn't get too charred.
Once both sides have been grilled, bring the dough inside to assemble your toppings. We usually do tomato sauce as our base, whole milk mozzarella, and pepperoni or sausage. It can be ANY toppings you want. We have even done a pesto base before.
Once you've assembled it, bring the pizza back outside, turn the grill to LOW and place your pizza creation on the grill. Close the lid and grill until the cheese is all melted and the ingredients have been warmed through.
Turn off the grill and bring your pizza inside to slice!