Add the warm water, active dry yeast, and sugar to a large mixing bowl. Stir gently and let sit for 5 to 10 minutes, or until the yeast begins to look foamy.
Add the sourdough discard and stir until mostly combined.
Add the flour, salt, 4 tablespoons of the olive oil, and rosemary. Mix until a sticky, shaggy dough forms.
Cover and rest for 30 minutes.
Perform a set of stretch-and-folds around the dough.
Cover and rest for another 30 minutes.
Perform another set of stretch-and-folds.
Cover and allow the dough to rise for about 1 to 1 ½ hours, or until noticeably puffy.
Spread the remaining olive oil over the bottom and sides of a 9x13-inch baking pan.
Transfer the dough to the pan and gently stretch it toward the corners.
Cover and let rise for 45 to 60 minutes, or until very puffy and bubbly.
Preheat the oven to 425°F.
Dimple the dough deeply with your fingertips.
Spread ¾ to 1 cup of pizza sauce over the dough.
Top with mozzarella, pepperoni, Parmesan, and optional seasonings.
Bake for 25 to 30 minutes, or until deeply golden around the edges and the cheese is melted and browned in spots.
Cool for about 10 minutes before slicing.
Top with fresh basil if desired and serve warm.