Place flour in large mixing bowl and whisk in dry instant yeast. Using a ricer, add the potatoes.
Add the lukewarm water and small pinch of salt to the flour and begin kneading to obtain a sticky, firm ball.
Place the dough in a bowl sprayed with vegetable oil. Wrap the top of the bowl with plastic wrap and let the dough rise until double in a warm, dry place. About 1 hour -- depending on the warmth of your kitchen it may take longer.
Preheat oven to 430 F.
Use the olive oil to generously grease a large baking pan ( we used a 12-inch pan) don't use any smaller or the dough will creep over the edge. Stretch the dough to evenly fill the pan.
Press the halved tomatoes in the dough, cut side down, add the olives, a generous sprinkling of Tuscan or Oregano seasoning and sea salt.
Drizzle the surface with more olive oil and bake in the hot oven for 20-30 minutes, or until the surface appears evenly browned and tomatoes are caramelized.
Lightly dust with Parmesan cheese when it is finished baking. Remove from baking sheet and let cool on a cooling rack.