This flatbread is made into thin strips instead of rounds, and they are eaten like open-faced sandwich boats.
Combine yeast with the warm water, sugar, and ¼ cup flour. Let sit 10 minutes. Add olive oil, cool water, salt, and ½ cup flour and combine with a wooden spoon. Add remaining flour and mix to form dough.
Knead dough on a floured board for 5 minutes, adding flour as needed to prevent sticking.
Let dough rise, covered, in an oiled bowl for 1 hour in a warm place. Punch down dough and divide into six pieces. Roll the pieces into balls and let rise, covered, for 1 hour.
Meanwhile, cut the onion into thin slices and gently sauté in the butter over medium-low heat until they are tender, 10 to 15 minutes. Salt them and set aside.
Preheat oven to 350°F. Roll out the dough into 10-inch-long by 2-inch-wide strips on a lightly floured surface. Place the strips onto a cornmeal-dusted baking sheet. Poke the strips with a fork all over.
Spread the sautéed onions over the dough strips and sprinkle the thyme over them. Put two anchovies and several olives on each flatbread and bake for 10 to 15 minutes, until crisp.