Prep your toppings! Chop anything that needs chopping, and have the topping ingredients lined up and ready to go.
Place the pizza stone in the pizza oven, or in the oven, and heat until the appropriate temperature is reached. If on the grill, light it up accordingly, put the grate in place, and top with pizza stone, allow to get to temperature. *Tip: For pizza ovens, temps should reach 750 - 900°F; for the grill ~ about 500 - 600°F; and for the oven ~ 450 - 550°F.
Start rolling out the pizza bases no more than 30 minutes before you are ready to cook them. Working with one pizza base at a time, on a lightly floured surface, roll or stretch out each pizza base until it's about 10 - 12 inches in diameter. *Tip: If you're making this in a pizza oven, for the best crust, it needs to be thin and about 8 - 10 inches in diameter for best results. I like to leave a rim around the edge that is a little thicker. I find it best to use a wooden pizza paddle that is lightly floured when topping my pizzas, as this makes transferring an aluminum pizza peel (for use with a pizza oven) or pizza stones much easier.
Once the base is ready, place on a lightly floured wooden pizza paddle or chopping board and start topping. Thinly sauce, add the torn prosciutto pieces, halved or chopped cherry tomatoes, torn or diced cheese, and if you wish you can also scatter additional fresh oregano or basil on top.
When the pizza oven, grill, or oven is at temperature, it's time to launch or transfer the pizza to the preheated pizza stone (it's best to leave the stones in place, do not try to remove them from the ovens).
In a pizza oven, after about 25 - 30 seconds, use the aluminum pizza peel to "grab" and pull out, rotate pizza, and place back in the pizza oven for an additional 25 - 30 seconds. Remove from the pizza oven.
On the grill, launch or transfer to the pizza stone, close lid and cook for 5 - 8 minutes, once ready, remove carefully.
In the oven, launch or transfer the pizza to the pizza stone, cook for 8 - 10 minutes or until the pizza starts to turn golden.