Place the warm water into a small bowl and dissolve the yeast in the water. Create a mound of 3 1/2 cups of the flour on a counter top creating a well in the center. Add 3 tablespoons of oil, warm water with yeast, and salt into the well. Work the mixture into a dough and knead it until it is soft, smooth, and elastic, using additional flour if dough is too sticky. Place the dough into a lightly oiled bowl and cover it with plastic wrap. Let rise for an hour, or until doubled in size. 
Preheat your oven to 400 F (180 C). Divide dough into two pieces and roll each out into very thin disks the size of your baking sheet. Lightly oil the pan and lay the first sheet of dough over it. Cut up the cheese into small pieces and sprinkle it over the dough. Lay the second layer of dough over the first, roll the edges up and around to form a rim that seals the cheese inside.  Brush the top with the remaining oil, and sprinkle with a little sea salt. Puncture the top here and there the moisture can escape as the focaccia cooks, and bake it for about 15  to 20 minutes, or until it's golden brown. Allow to cool 10 to 15 minutes, and slice into wedges with a pizza cutter. Serve warm.