Measure the warm water into a 2-cup liquid measuring cup. Sprinkle the yeast over the top and let it sit until it’s frothy and mostly dissolved, about five minutes.
Meanwhile, in the bowl of a stand mixer fitted with the paddle attachment, combine the bread flour and salt, mixing briefly with the beater attachment to blend.
Add the room temperature water and olive oil into the measuring cup with the yeast. With the mixer on low speed, pour the yeast mixture into the flour mixture. Mix until a cohesive dough is formed and the dough starts to pull away from the sides. Switch to the dough hook, then knead on low speed until the dough is smooth, shiny, and elastic, about 4-5 minutes.
Transfer to a lightly oiled bowl, turning once to coat. Cover with plastic wrap and let rise in a warm spot until doubled in size. On a very warm day, this may only take an hour. Some days it’s closer to 2.
Punch down the dough to deflate it. Flour your hands and a workspace. Transfer the dough to your workspace and divide the dough into two equal pieces. Form each piece of dough into a smooth, round ball.
Place a pizza stone in the oven and preheat it as high as the oven will go (usually 500 degrees).
Shape the pizza dough on either a piece of parchment paper or a pizza peel.
Place the dough in the center of the parchment and use the heel of your hands to gently push the dough out from the center. As it gets thinner, you can use your fingers to continue to stretch it into a 12 inch circle. You can either use your fingers to create a raised crust, or fold over the outer edge to create a thicker outer crust. If the dough continues to spring back, cover it with a damp cloth and let sit for 15 minutes then try again.
Brush with olive oil and add any seasonings or toppings you wish. To bake, place the parchment on a flat cutting board or baking sheet. Use a forward flick of your hand to transfer it to the pizza stone. Bake for 12-15 minutes or until crust is puffed and golden brown and toppings are hot and bubbly.
Notes
See the post body for detailed instructions on shaping, extending the rise time, freezing, and thawing pizza dough.