In a large mixing bowl, combine the sourdough discard, warm water, optional instant yeast, and optional granulated sugar. Stir gently to dissolve the yeast and sugar (if using yeast). Let it sit for 5-10 minutes until slightly foamy if using yeast; otherwise, just stir to combine.

Add the flour, 2 tablespoons of olive oil, and fine sea salt to the wet mixture.

Using a sturdy spatula, dough whisk, or your hands, mix until a shaggy dough forms and no dry flour remains. If the dough is too dry, add a tiny bit more water (1 teaspoon at a time). If too wet, add a sprinkle of flour. The dough will be slightly sticky.

Turn the dough out onto a lightly floured surface. Knead for 5-7 minutes until the dough becomes smoother and more elastic. It doesn't need to be perfectly smooth like a traditional pizza dough, but a short knead helps develop gluten. Alternatively, if you prefer a no-knead method, simply ensure all ingredients are well combined and proceed to the next step.

Lightly oil the mixing bowl (the one you used initially). Place the dough back in the bowl, turning it once to coat with oil. Cover the bowl with plastic wrap or a damp kitchen towel and let it rest in a warm place for 60-90 minutes, or until it has noticeably puffed up (it won't double like yeasted dough, but should show good activity).

About 20-30 minutes before baking, preheat your oven to 475°F (245°C). If using a pizza stone or steel, place it in the oven during preheating. If using a baking sheet, you can place it in the oven to preheat inverted for a crispier crust, or prep it directly. Lightly flour two pizza peels or large pieces of parchment paper.

Gently turn the dough out onto a lightly floured surface. Divide the dough into two equal portions for two medium (10-12 inch) pizzas. Working with one piece at a time, gently stretch or roll the dough into your desired pizza shape. If the dough springs back, cover it and let it rest for 5-10 minutes, then continue stretching.

Carefully transfer the shaped dough onto the preheated pizza stone/baking sheet (or onto parchment paper first, then slide onto the hot surface). Quickly add your desired pizza sauce, cheese, and toppings.

Bake for 10-15 minutes, or until the crust is golden brown and the cheese is bubbly and slightly browned. Baking time will vary based on your oven and topping quantity. For best results, rotate halfway through if your oven bakes unevenly.

Remove from the oven, let cool for a minute or two on a wire rack to prevent a soggy bottom, slice, and serve immediately. Repeat with the second dough portion.