Either in the microwave or in the oven, cook the sweet potato until it is softened throughout. Remove the skin, mash the potato, and set aside.
In the bowl of a stand mixer fitted with the whisk attachment, whisk together the yeast and ¼ cup / 60g of the lukewarm water. Let it sit for 3 to 5 minutes or until it swells up slightly. Add the flour, kosher salt, and the remaining 1 ¼ cups / 300g lukewarm water.
Snap on the dough hook and mix the dough on low for 2 minutes. It should look very wet, almost like batter. Add ½ cup / 115g of the mashed sweet potato and mix again until the potato is fully incorporated. Cover the bowl with a towel and let it rest for 10 minutes.
Mix on medium-high speed until the dough pulls away from the sides of the bowl and is elastic enough to pull up in a long stretch, 12 to 1 7 minutes. It will take some time, so don't worry.
Place the mixed dough in an oiled bowl. Cover this and let it rise until doubled in size, about 1 hour.
When the dough is ready, add 3 tablespoons olive oil to a 9½ by 13-inch quarter-sheet pan. Rub the oil all over to coat the pan. Plop the dough in the center and use oiled fingers to pull it to the edges of the pan. It will be pretty elastic and pull back but don't worry about that. Let it rest for 5 to 10 minutes to let the gluten relax, then pull the relaxed dough out to the edges. Cover with oiled plastic wrap or a loose-fitting lid and let the dough rise until it has bubbled to the top of the sheet pan, about 1 hour.
Preheat the oven to 425F.
When the dough has risen, drizzle with at least 2 more tablespoons of olive oil and use your fingers to dimple the dough all over. Sprinkle with the flaky salt and bake until golden brown, 20 to 25 minutes.
Slice into eight rectangles, each approximately 3 ¼ by 4 ¾ inches in size, and serve warm.