Steps

1. Add the warm water and yeast to the bowl of an electric mixer, stir once and let set ten minutes. Stir about 1/3 of the flour into the yeast mixture, cover with plastic wrap and set in a warm (80-85°F) place for 45 minutes.
2. Add the remaining flour, 1/4 cup of the olive oil and salt and stir in with a wooden spoon or spatula. Transfer the bowl to the mixer and mix on low speed with the paddle attachment until all the flour is moistened. Increase speed to medium and beat another 2 minutes. Scrape down the bowl and paddle and mix on low speed another two minutes. Set aside to rest.
3. Grease a 12x18-inch baking sheet with olive oil and line with oiled parchment paper. Using oiled hands, transfer the focaccia dough to the baking sheet. Gently flatten out the dough, taking care not to rip it.
4. Lightly brush the remaining olive oil over the top of the dough, cover loosely with plastic wrap and set in a warm place for 30 minutes.
5. Press the dough out to fill the baking sheet. Cover loosely with plastic wrap and set aside to rest another 30 minutes.
6. Spread the potatoes slices evenly over the top of the focaccia and sprinkle with the rosemary, cheese, salt and pepper. Gently dimple the dough at several places with your finger, cover loosely with plastic wrap and rest a final 30 minutes.
7. Preheat oven to 425°F and set a rack in the center of the oven. Set the focaccia in the oven, reduce heat to 375°F and bake until golden brown and the center of the dough springs back, 17-20 minutes. Remove, cool on a rack and cut into individual pieces.

Notes

True focaccia has an uneven crumb structure, with some small holes and some large. Use bread flour to achieve this result. All-purpose flour will produce a smaller, more even crumb.