Whisk the flour and salt together in the bowl of a stand mixer. In a separate bowl, whisk together the warm water and the yeast and let sit for 5-10 minutes (if using instant active dry yeast, you can eliminate the resting time). Whisk the oil into the water/yeast mixture and then pour the liquid into the dry ingredients.
Mix on low speed until the ingredients are combined and the dough is smooth, about 2-3 minutes. It will be very soft and sticky. Cover the dough with plastic wrap and set it aside on the counter to ferment until the dough doubles in size, about 30 minutes.
Spread a generous amount of olive oil on a half-sheet pan (12x16-inch) and turn the dough out onto the pan. Coat your hands with some oil to prevent sticking, and stretch the dough to the edges of the pan. Pierce the dough all over with your fingertips, making deep indentations. This process is called dotting the dough. Brush the surface with olive oil and add your desired toppings. Sprinkle with coarse salt. Cover with plastic wrap and set aside in a warm place to proof until doubled.
I decided to make half of my focaccia with tomato, basil, and garlic and the other half with potatoes, rosemary, and garlic. Spread the minced garlic over the entire surface of the dough. Then on one half, arrange the tomato slices over the top. On the other half, sprinkle on some rosemary, then arrange the potato slices over the top. Sprinkle some more rosemary on top.
Bake the focaccia in the oven at 450 degrees for about 20 minutes, until it is a light golden color and cooked through. If using fresh basil, sprinkle it on about a minute before you take the focaccia out of the oven so that it doesn't burn. Slide the focaccia onto a wire rack and cool before cutting into pieces and serving.