In the bowl of an electric stand mixer whisk together active dry yeast, sugar and 1/2 cup water. Let rest 5 - 10 minutes until it starts to bubble up. If using instant yeast see notes as method is different.
Add in remaining 1 cup warm water, 3 Tbsp olive oil, salt, and 3 cups flour. Set mixer with paddle attachment and blend mixture until combined.
Switch to a hook attachment, then knead in remaining 1/2 cup flour. Continue to let knead, while adding more flour 1 or 2 Tbsp at a time as needed until dough isn't overly tacky.
Knead on medium-low speed about 6 - 8 minutes until dough is soft and supple and pulls away from the sides of the bowl. Dough should be just slightly sticky.
Transfer dough to a large oiled bowl (preferably coated with olive oil or olive oil cooking spray), turn dough to other side to coat opposite side in oil.
Cover bowl with plastic wrap and let rest until double in volume in a warm place about 1 1/2 hours, or even better 24 hours in the fridge if time allows. If using the fridge method, the following day you'll need to let the dough come to room temperature for about 1 hour before shaping.
Near end of rising place pizza stone in oven and let preheat to 475 degrees for 30 - 45 minutes.
After rising, press dough down, divide into two portions (freeze** second portion for later at this point if desired).
Place each portion if using both right away into two oiled bowls, cover and let rest 15 minutes.
Stretch and shape dough into a circle about 11 - 14 inches depending on how thick or thin you like the crust.
Transfer to a sheet of parchment paper just large enough to fit.***
Brush top of crust with olive oil (about 1 Tbsp each). At this point for a fluffier crust if preferred, let rest 10 minutes. Spread top with sauce (I use about 2/3 cup), sprinkle with cheese (I use about 2 cups mozzarella) and finish with desired toppings.
Transfer with parchment paper to preheated pizza stone and bake until crust is golden brown and cooked through, about 11 - 14 minutes.
Slice and serve pizza warm. Repeat process with second dough if using.
*If using instant yeast:
**Dough can be frozen, to do so:
***Parchment paper should be trimmed to fit the crust or removed partway through baking so it doesn't scorch. Also at this point to reduce bubbles if desired, you can press fingertips randomly over shaped dough or pierce randomly over top with a fork.
Nutrition estimate is for dough only. No toppings.
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