Combine warm water, sourdough discard, olive oil, sugar/honey, and yeast in a large bowl. Stir until mostly smooth.
Add flour and salt. Knead 6-8 minutes by mixer or 8-10 minutes by hand until soft and slightly tacky.
Place dough in oiled bowl, cover, and let rise until doubled (1-2 hours with yeast, up to 4 hours without).
Punch down dough, divide into 2 balls, shape smoothly, and rest 15-20 minutes.
Preheat oven to 475-500°F with pizza stone if using.
Stretch one dough ball into a 12-inch circle on semolina-dusted surface. Leave thicker edge.
Transfer to peel or sheet. Add thin layer of sauce, cheese, and light toppings.
Bake 10-15 minutes until crust is golden and cheese bubbles. Cool 2 minutes before slicing. Repeat with second ball.