Combine the water, sugar, and yeast in the bowl of a standing mixer fitted with the dough hook and let the mixture sit until it becomes foamy, about 5 minutes.

Add the flour, oregano, mashed potato, 3 tablespoons of the olive oil, and the salt to the yeast mixture and mix on low speed for 10 minutes, scraping the dough and the hook about halfway through. The dough will come together and begin to pull away from the bowl. (alternatively, you can mix the dough with a wooden spoon in a wide, shallow bowl. Once you stir everything together, transfer the dough to a lightly floured surface and knead until smooth, about 10 minutes.)

Transfer the dough to a lightly floured work surface and knead it several times with floured hands to form it into a bowl. Put the dough in a lightly oiled large mixing bowl, turn the dough so that the entire surface is lightly oiled, cover the bowl with plastic wrap and set it aside in a warm, draft-free place until the dough has doubled in size, about 1 hour. Punch down the dough, recover the bowl, and set it aside again to rise a second time, until doubled in size, about 1 hour.

While the dough is rising, make the Tomato Sauce and set aside. Line a 12- by 17- by 1-inch deep baking sheet with parchment paper and lightly oil the parchment.

Transfer the dough to the lined baking sheet and press the dough down with your fingers, then press and stretch it so that it fills the pan in an even layer.Lightly coat the top of the dough with olive oil, cover with plastic, and set aside to rise until doubled a final time, about 1 hour.

Preheat the oven to 450° F.

Uncover the dough and, using your fingers, gently dimple the dough all over with your fingertips, leaving indentations about 1/2-inch deep. Spoon 2/3 cup of the tomato sauce evenly over the dough. Sprinkle with the 1/2 teaspoon kosher salt, then sprinkle with the Caciocavallo cheese. Sprinkle the chopped anchovies evenly over the top of the dough. Place the breadcrumbs in a small bowl and combine with the remaining tablespoon of olive oil. Sprinkle the crumbs evenly over the top of the dough.

Bake the focaccia until golden brown, risen, and crumbs are evenly browned, 15 to 20 minutes. Let cool briefly before cutting into squares and serving with additional sauce and/or shredded cheese, as desired.