Preheat oven to 230°C / 450°F. Place a cast iron pan inside and let it heat for 20–30 minutes.
Remove the hot pan, drizzle in olive oil, and swirl to coat the surface.
Add the sourdough discard to the pan and carefully spread it thinly using a spatula.
Drizzle a little more olive oil on top and sprinkle with salt or herb salt. Add cherry tomatoes if using.
Bake for 5 minutes to partially cook the crust.
Remove from oven, sprinkle with shredded parmesan, and crack eggs on top. Add green onions and fresh oregano.
Return to the oven and bake for another 5 minutes, or until egg whites are set but yolks remain soft.
Remove from the oven and add a spoonful of pesto and a final drizzle of olive oil before serving.