Combine yeast with 1/4 cup of lukewarm water. Allow to sit for a few minutes.
To bowl of a food processor fitted with steel blade, add flour, 1 teaspoon salt, 6 tablespoons olive oil, yeast-water mixture, and 3/4 cup of lukewarm water. Process, about 20 seconds, until dough forms a smooth ball. Turn dough onto smooth surface; knead for a couple of minutes, adding flour if too sticky.
Place dough in oiled mixing bowl. Cover with plastic wrap; let rise in warm place until doubled in size, about 30 minutes.
Set rack in lower third of oven. Preheat to 450° F.
In 9 x 12 inch baking pan, spread one and a half tablespoons olive oil. Turn dough into pan; press with fingers to fill pan completely. Cover with plastic wrap; set in warm place to rise until doubled, about 30 minutes.
Dimple top of dough with fingers, brush with olive oil, sprinkle with chopped tomatoes, sea salt, oregano, and Parmesan. Drizzle on a little more oil. Place baking pan on cookie sheet and bake 20 - 25 minutes, until golden. If serving immediately, slide focaccia onto cutting board. If serving later, cool on a rack.