Place the sourdough starter, sugar, and water in the bowl of a stand mixer. Using the paddle attachment, mix until mostly dissolved and a light foam forms.

Switch to the dough hook and add the all-purpose flour, semolina flour, mashed boiled potatoes, and salt. Begin kneading the dough.

After a few minutes, slowly drizzle in the extra virgin olive oil while continuing to knead for about 10-15 minutes.

Transfer the dough to a bowl, cover well with a kitchen towel, and let it rest at room temperature for 1 hour.

Place the dough in the refrigerator and let it rise for 36 hours.

After this time, remove the dough from the refrigerator and let it sit at room temperature for 2 hours to come to room temperature.

Arrange halved cherry tomatoes, cut side down, over the surface of the dough. Do this over the pans so any juices fall directly onto the dough.

Make the brine by whisking together the water, extra virgin olive oil, and dried oregano.

Remove from the oven and serve warm or at room temperature—delicious either way!