Combine the flour, salt, sugar and yeast in the bowl of a stand mixer.
Combine the sourdough starter or discard, water and olive oil in a second bowl. Stir to dissolve the starter in the liquid.
Add the liquid ingredients to the dry ingredients and mix with the dough hook on low speed until a dough is formed. Add more flour or water as needed so that the dough stays together. Let the mixer knead the dough for about 10 minutes. The dough should clean the inside of the bowl.
Place the dough in a lightly oiled bowl and let it rise in a warm place (around 75˚F), covered with plastic wrap or a clean kitchen towel, until it has doubled in bulk. This should take an hour or two.
Turn the dough out onto the counter and divide the mixture into two dough balls, shaping them into rounds with your hands. Lightly coat each dough ball with oil and transfer to the refrigerator, covered with plastic wrap. You can place them on a baking sheet, or place each dough ball into its own oiled zipper sealable plastic bag or container. (You can freeze the dough balls at this stage, removing as much air as possible from the oiled bag.) Keep in the refrigerator for at least one day, or as long as five days.
When you’re ready to make your pizza, remove your pizza dough from the refrigerator at least 1 hour prior to baking and let it sit on the counter, covered gently with plastic wrap.
Use the dough to make pizza, calzone, stromboli or any other recipe that calls for pizza dough.