The dough makes enough for 2 focaccia breads. You can freeze half of the dough for another date.
Weigh or measure out the flour into a large mixing bowl. On one side of the bowl add the salt and on the other side of the bowl add the yeast.
Add the olive oil and about 2/3 to 3/4 of the water. Mix ingredients together with your hands. Add more water about a tablespoon at a time, if the dough is too dry. You are looking for a wet sticky dough that sticks to your fingers but not "mushy wet" like a batter. You may not end up using all of the water. This dough starts out wetter than a standard bread dough.
Lightly dust your counter top with flour.* Knead the dough for 5 to 10 minutes until you have a soft but smooth elastic dough with only a slight stickiness to it. It starts out really sticky and will stick to your work surface, but after about 3 minutes of kneading you will see it become smoother and less sticky. Try not to add more flour, just keep at it! Video - How to knead bread dough.
Shape the dough into a nice ball and put it into a large oiled bowl or an oiled plastic container. Cover with a tea towel and let it rise until doubled in bulk. Approximately 1 to 2 hours. It all depends on the temperature of your home and unexplained forces of nature.
Prepare your pan - liberally oil 2 baking sheet pans with olive oil.
Place the risen dough on to a lightly floured counter top. Gently shape into a thick rectangle and then cut the dough in half. Do not knock the dough down as you are trying to keep as much air as possible in the dough.
Take one of the dough pieces and with your hands, press and stretch the dough out in a even layer, into the desired shape of the focaccia. The shape can be irregular, which is fine because now it looks rustic. :) Place the dough on to the prepared sheet pan. Shape it a little more if you want. Do not stretch it to the edges of the pan. You want a thick dough. Mine was around 13" x 10". Cover with plastic wrap or a large tea towel. Repeat with second half of dough *See notes if you want to freeze second piece of the dough for a later date.
Let the dough proof until it is doubled in size for about an hour. It's a little hard to tell when it has doubled, but it will definitely look "puffier".
While the dough proofs, preheat your oven to 400°F. Slice or chop the onion and saute it in a little olive oil until soft. Do not let the onion brown. Set aside.
When the dough has proofed, make your first focaccia. Generously drizzle 1 to 2 tablespoons of olive oil over the top and gently rub the oil to spread it out evenly. Take half of the grape tomatoes and place them around the dough's surface. Press them firmly into the dough so they stay in place.
Bake for 15 to 20 minutes or until the foccacia is a light golden brown. The bottom of the bread should sound hollow if you tap it. Drizzle some more olive oil over the top and then it let cool on a wire rack. Cut into desired size pieces to serve.