Mix together the fresh sourdough starter, one tablespoon of oil, the salt and 1-1/4 cups of flour. Add more flour, a little at a time, as needed to form a pizza dough consistency. The amount of flour needed will depend on the hydration level of your sourdough starter (the flour-to-water ratios used when feeding the starter).
Allow the dough to rest for 30 minutes as it will be easier to roll out. (It won't rise significantly, if at all.) Roll the dough out into a circle using a minimum amount of flour to prevent sticking.
Bake the crust for approximately 7 minutes.
Remove the crust from the oven and brush on the remaining oil to prevent the toppings from soaking into the crust and making it soggy.
Add the desired toppings and bake the pizza until the crust browns and the cheese melts.