Peel and dice the potatoes; cook them in boiling water for 20-25 minutes or until tender.
Let the potatoes cool down a little and then mash or rice them for a more uniform texture.
Dissolve the yeast in 10 tablespoons (150ml) of lukewarm water and add the sugar to active it.
Sift the two types of flour together; add the salt and the mashed potatoes.
Mix it all with a stand mixer, like a KitchenAid, fitted with a dough-hook attachment or by hand on a flat surface. Mix it until smooth and even.
Pour in the water along with the yeast and knead it carefully.
Gradually add 2 tablespoons of oil, one at a time.
Knead it with your hands or in a stand mixer at medium speed; don’t worry if the dough doesn’t come together, it will after you pour in some more water.
Pour in the water until it’s a soft and almost sticky mixture.
Knead it a couple of minutes until it becomes stretchy; the dough should release easily from the side of the bowl and twist around the hook; just don’t knead it too long.
Pour it onto a floured surface and sprinkle the dough and your hands with all-purpose flour; shape the dough into a rectangle and then fold the two sides into the center and then fold it again laterally.
When a smooth dough has formed, make a ball with floured hands and place it in the oiled bowl.
Cover the bowl with plastic wrap and let it rise until the dough has tripled in volume.
In the meantime, halve the tomatoes and dress them with salt, oil, and oregano; set them aside; a little liquid will be released.
Put the dough into an oiled round 10-inch (26-28cm) pan; flatten it with the tips of your well-oiled fingers.
Place the tomatoes and black olives spaced evenly on the surface and press them into the dough. Pour a little tomato liquid for a more flavorful taste.
Generously season it with extra virgin olive oil, dry oregano, and coarse salt.
Let the flatbread rise for one hour or until it has doubled in volume; the tomatoes and olives will have sunk into the dough.
Pre-heat the static oven to 400°F (200°C) and bake for about 25 minutes: first place the tray onto the lower rack for 10 minutes; then move it to the middle for the remaining 15 minutes.
Check for doneness: the edge should be crunchy- take it out of the oven and let cool down a bit before serving. This scrumptious flatbread is ready to be eaten either hot or cold.