Thoroughly mix the two cheese together in a bowl. Divide the dough into 12 even spherical portions. Roll each ball into a 4-inch circle, about 1/16-inch thick. Place a spoonful of the cheeses in the center of each piece of dough, then fold one edge over to form a half-moon shape. Pinch the edges to seal them and prevent the cheese from seeping out during cooking. Place the oil in a heavy-bottomed pot. Test the oil to determine whether it's ready for frying by dropping a small piece of dough into the pot. If the piece floats right away with bubbles all around it then the oil is ready. Fry the pizzelle until golden brown on both sides. Drain on paper towels. Serve immediately.
Mix 1 tablespoon of the water, the sugar, and 1/8 teaspoon of the yeast into a small bowl. Place one third of the flour in the mixing bowl of a mixer with the hook attachment. Add the warm water, olive oil, dissolved yeast, egg, and salt and mix for 5 minutes on low speed. Fold in another third of the flour and continue to mix for another 5 minutes on slow speed. Add the remaining flour and the remaining 1/8 teaspoon of dry yeast, increase the speed to medium, and continue to mix for an additional 5 minutes. Place the dough in a lightly oiled bowl, cover with plastic wrap, and allow to rest in the refrigerator for 1 hour. Divide the dough into six 7-inch circles, approximately 4 ounces each. Rub your hands with a little oil so the dough won't stick to your fingers. Place the dough on a lightly oiled cookie sheet, cover well with plastic wrap, and let them rest in a warm place for another 3 hours. Flatten and form the dough into 12-inch circles, add the desired toppings, and bake according to the recipe. The dough can be wrapped in individual-pizza portions and refrigerated for up to 5 days, or it can be frozen.