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Mound flour on a table and make a well in the center. Pour the dissolved yeast, oil, and salt into the center of the well. Gently mix in flour with a fork. Dough should be smooth and pliable. Add warm water if dough is too dry. Roll the dough into a ball and put in an oiled bowl. Cover with a cloth and put in a warm place for 1 hour.
Divide the dough into 2 pieces and roll out 1 of the dough balls into a round shape, about 12 inches in diameter and 1/4-inch thick. Lay in a greased 12-inch tart pan with a removable bottom.
Spread the tomatoes, mozzarella, ham, and pecorino on the dough. Sprinkle with oregano, salt and pepper. Roll out the other ball and lay it on top, folding the top and bottom layers of dough together around the edges. Cut 3 small holes in top of the pie for steam to escape. Bake in the oven until the crust is brown and the cheese is melted, about 20 minutes.