In a large bowl, stir yeast into water to soften. Add salt, garlic, rosemary, olive oil, potato, cheese, and 3 cups flour. Beat vigorously for 2 minutes. Gradually add flour, 1/4 cup at a time, until the dough begins to pull away from the side of the bowl.
Turn dough onto a floured work surface. Knead, adding flour a little at a time, until you have a smooth, elastic dough. Place dough into an oiled bowl. Turn to coat the entire ball of dough with oil. Cover with a tightly woven towel and let rise until doubled, about 1 hour.
Turn dough out onto a lightly oiled work surface and divide in half. Shape each half into a ball and place onto a well-greased baking sheet. Cover with a tightly woven towel and let rise until almost doubled, about 45 minutes.
About 10 minutes before baking, preheat oven to 375 degrees. Place a shallow pan on the bottom shelf of the oven. Just before baking, brush each loaf liberally with extra olive oil and cut a cross about 1/4-inch deep into the top. Place the bread in the oven and put 5 ice cubes into the pan on the bottom shelf. Close the door quickly to prevent steam from escaping. Bake for 25 minutes, or until the internal temperature of the loaves reaches 190 degrees. Immediately remove bread from baking sheet and cool on a rack.