Combine Ingredients: In a large bowl of a stand mixer combine 1/2 cup of the warm water with the sugar and yeast. Stir to dissolve the yeast and let rest for 5 minutes. It should foam on the top. Add the remaining 1 cup of warm water, olive oil, salt and vinegar.
Knead Dough: Begin mixing on medium-low speed, gradually adding the flour a cup at a time, and knead the dough for about 7 minutes, or until it's smooth and elastic. You may not need all of the flour. The dough should be slightly sticky, but not so sticky that it really sticks to your fingertip when touched.
Rise: Transfer dough to a greased bowl and cover with a dry towel or greased plastic wrap. Allow to rise for 1 to 1.5 hours, or until it has about doubled in volume.
Roll out: Gently punch the dough down and place on a lightly greased or floured counter top. Divide dough into 2 or 3 equal pieces (makes about two 14'' or three 9'' pizzas). Roll and stretch the dough to desired size and thickness. Brush dough with olive oil.
Preheat oven to 450 degrees F (with a pizza stone inside, if you have one). Add cornmeal and flour to a pizza peel or use a pizza pan. Pick the top of the dough a few times with a fork and pre-bake the dough in the pizza pan, or slide onto a hot pizza stone to pre-bake for 3-4 minutes. Remove from oven and add pizza sauce and toppings. Return to oven and bake for 8-15 more minutes or until the crust is golden and the cheese is bubbly.
Pizza Oven Method:
Add cornmeal and flour to a pizza peel and place rolled out dough on top. Add toppings. Slide into preheated pizza oven and cook according to pizza oven instructions.
Air Fryer Method:
Roll dough into small sizes that will fit in air fryer. Cook in air fryer for 1 minute (check after 30 seconds, to make sure it didn't fold over), then flip sides and cook 1 more minute. Repeat with remaining crusts. Add toppings. Cook at 370 for 1-3 minutes or until bubbly.
Preheat grill to medium-high. Roll out dough and place on a piece of parchment paper. Spread with oil, then gently flip the pizza onto the grill, oil side down, and peel the parchment paper off. Cover grill lid and cook for 2-3 or until grill marks on bottom. Flip the pizzas onto a plate and add sauce and toppings to cooked side. Reduce heat and slide pizzas back on frill to cook another 3-5 minutes.
Pre-Bake Dough, if cooking pizza in the oven. If you're baking the pizza in the oven, whether on a pizza stone or not, I always pre-bake the dough for 4-5 minutes before adding toppings, to make sure the pizza dough cooks crisp on the outside and soft and airy in the middle. Once you add the Pizza Sauce and toppings, return it to the oven to finish baking.Make Ahead Instructions: mix the dough, place in a large greased bowl with a tight lid and refrigerate for several hours, or even overnight. Remove from the fridge and allow to come to room temperature so it's easy to roll out. You could also roll-out and pre-bake the dough, add toppings and store in the fridge for a take-and-bake style pizza.Freezing Instructions: once the dough is mixed, wrap it in plastic wrap and place it in a freezer safe container to freeze for up to 3 months. When ready to thaw, place it in a greased bowl, covered, in the fridge until compeltely thaw (about 24 hours). Allow to come to room temperature so it's easy to roll out. You could also freeze the pre-baked dough, with or without toppings.