makes dough for four individual pizzas, 12-inches each; adapted from Peter Reinhart's Pizza Napoletana in The Bread Baker's Apprentice and Maurizo Leo's Sourdough Pizza Dough from The Perfect Loaf
Measure water into glass measuring cup, ensure it is not too hot or it will kill the yeast. Sprinkle the yeast into the water, add the sugar or honey, stir and let stand until creamy, about 5 minutes. (If your yeast is instant, you do not need to proof it. Just mix everything together and proceed with the next step.)
Using an electric stand mixer mix the flour, sourdough starter, olive oil, salt, and the contents of your yeast-sugar/honey-water measuring cup until combined (paddle or dough hook), then turn off the mixer and let dough rest 5 minutes.
Knead 5 minutes using the dough hook until you have a smooth dough that actively gathers around the hook.
If the dough is too wet and doesn't come off the sides of the bowl, sprinkle in some more flour just until it clears the sides. If the dough is too dry, dribble in additional water a tablespoon at a time.
Shape dough into a ball and transfer to an oiled bowl. Cover and allow to rise for 60–90 minutes.
Divide dough into 4 equal pieces and gently round each into a ball. Lightly oil the surface of each and transfer to a covered container to rest until an hour or two before pizza baking time.
Remove the dough balls from the refrigerator one to two hours in advance of pizza making time.
Lightly dust counter with flour, flatten each dough ball slightly, loosely cover with plastic wrap, and let rest for an hour or two.
If you have a pizza stone, place it in the oven. Preheat oven to 475°F.
If you do not have a baking stone, you can use the back of a sheet pan or a pizza pan. Do not preheat the pan, just get the oven nice and hot.
Working one at a time, turn dough upside down and using your hands in a "V"-shape, lightly press the dough from the center towards the edge, leaving the edge untouched to create a puffy edge of dough around the pizza. Flip and repeat on the other side.
Transfer the dough to your fists and work to gently stretch and ease the dough close to 12-inches in diameter. Transfer to a pizza pan or piece of parchment paper.
Lightly top each pizza with sauce, cheese, and toppings using a less less-is-more philosophy. Slide each pizza in turn onto the stone (or put pizza pan or pizza-topped sheet pan in oven) and bake 8–10 minutes. Slice, or not, and eat!