Step 1In a small bowl, stir together the yeast, water and vegetable oil until combined.
Step 2In a large bowl, whisk together the flour and salt. Stir in the yeast mixture to form a medium-soft dough, then turn the dough out onto a lightly floured board and knead until smooth and satiny, about 10 minutes. Place the dough in a large greased bowl, loosely cover with a towel and set aside in a warm place until risen and doubled in bulk, about 45 minutes.
Step 3While the dough is rising, in a large, heavy skillet combine the onions, garlic and 2 tablespoons olive oil. Loosely cover the skillet and cook slowly until the onions are tender and golden but not browned, about 40 minutes, stirring occasionally.
Step 4Put the tomatoes in a large, heavy saucepan and bring to a strong simmer over high heat. Reduce the heat to maintain a simmer and cook until the tomatoes break down and thicken, stirring frequently, 20 to 25 minutes.
Step 5Heat the oven to 400 degrees. Punch down the dough, then place on a lightly floured board and set aside to rest, covered with a towel, for about 5 minutes. Roll out the dough to make a circle 15 inches in diameter. Lift it onto a 15-inch pizza pan.
Step 6Sprinkle the dough with the grated Parmesan cheese.
Step 7Season the onion mixture, to taste, with salt and pepper. Spoon the onion mixture over the cheese-topped pastry.
Step 8Season the tomato mixture with the rosemary, salt and pepper, to taste. Spoon the tomato mixture over the onions.
Step 9Crisscross the entire pie with anchovy fillets and place an olive in each square.
Step 10Brush the olives with oil and bake until the crust is browned and the filling bubbly and hot, 15 to 20 minutes. Serve sliced.