Add the flour, salt, and yeast to a large bowl. Stir to combine. Add the water and olive oil. Use a rubber spatula to stir until no streaks of flour remain, about 3 minutes.
Cover and let the dough rise in a warm spot. After 30 minutes, perform a set of stretch and folds: Stretch: With slightly wet hands (to prevent sticking), reach under one side of the dough and gently stretch it upwards. You want to pull the dough without tearing it, stretching it to a point where it begins to feel slightly resistant.Fold: Once you’ve stretched the dough, fold it over towards the center of the bowl. The goal is to gently fold the dough onto itself.Rotate: Turn the bowl 90 degrees, and repeat the stretch and fold technique on the next side of the dough. Continue for the full 360 degrees of the dough. Cover the dough and let rest an additional 30 minutes. Repeat the process until the dough has rested a total of 2 hours, and 4 stretch and folds have been performed.
During the last stretch and fold, add about 1/4 cup of cheese in between each fold, layering the cheese throughout the dough.
After the last stretch and fold, throughly grease a 9x13-inch pan. Add 1 tablespoon of olive oil in the center of the pan.
Transfer the dough to the pan and coat the outside in the olive oil. Gently press down to stretch the dough better fit the pan, just the general shape — it shouldn’t stretch across the whole pan yet.
Cover the pan (with plastic wrap or a light kitchen towel) and let it rise for about 2 hours, or until it has doubled in size/fills the pan.
While the dough is rising, prepare the onions. Thinly slice the onions. Add the olive oil to a large pan over medium-low heat. Add the onions the pan. Cook, stirring occasionally, for 20-30 minutes, until the onions have turned a deep amber color. If the onions start to burn, turn down the heat and add a splash of water to get up any of the burned bits off the pan. Once the onions are caramelized, transfer to a plate to cool off completely.
Once the onions are cooled and the dough has finished rising, preheat the oven to 450F. Drizzle the remaining tablespoon of olive oil across the top of the dough. With lightly oiled fingers, make several dimples in the dough. Sprinkle the remaining 1/2 cup of cheese across the top, followed by the caramelized onions. Add a pinch of flaky salt across the top (optional).
Transfer to the oven and bake for 15 minutes, then lower the temperature to 425F and bake another 10-15 minutes, until the top is deeply golden brown. Carefully transfer the dough to a cooling rack to cool completely. Enjoy!!